Datamining project
phase 1
Problem statement
The dataset aims to identify and evaluate the severity of depression and anxiety among undergraduate students at the University of Lahore. The problem revolves around understanding the impact of depression and anxiety on students’ studies and social behavior
Data mining task
The task involves utilizing the dataset as a basis for evaluating different machine-learning methods and approaches, particularly for the classification of the severity of depression and anxiety.
Additionally, the dataset is suitable for comparing different machine-learning classification approaches to identify effective strategies for addressing mental health issues among students.
Goal
Our main goal in collecting “Depression and anxiety” dataset is to learn more about the number of college students facing difficulties that end them up in having particular disorders , in our case depression and anxiety . We gather information about their school year, depressiveness, anxiousness, and Sleepiness. This kind of data will help collages make generally better decisions about their academic plans to what is more suitable for the students ,and also help the student affairs deanery improve its services or even add more to fulfill what a college student needs. It could also help mental health hospitals in knowing the importance of how to raise awareness in college students about their mental health sanity which could decrease the risk of college students developing depression/anxiety.
Here are three specific goals we have for this dataset: 1. Classification Goal:
We want to group students into different categories based on their PHQ Score, GAD Score, and EPWORTH Score. By doing this, we can see patterns and trends among different groups. This will help us understand if these specific scores have to do with students developing depression/anxiety. With this information, we can develop strategies that could help ensure lower the risks of developing depression/anxiety.
- Defect Prediction Goal:
We want to use statistical techniques to seek trends that can predict any early symptoms of depression/anxiety. This could include things like, depressiveness, anxiousness, or Sleepiness. By catching these problems early, we can fix them and make sure students get help and achieve guidance toward the right path. This analysis will help make students mental health more “considerable”.
- Clustering Goal:
We’re clustering students together based on their similarities to create distinct clusters. Various methods will be utilized to determine the number of clusters that best suit our dataset, followed by evaluation techniques to assess the effectiveness of these clusters in segmenting the data effectively based on their inherent features.
Dataset Details:
Source of the dataset: Kaggle
Dataset Link: https://www.kaggle.com/datasets/shahzadahmad0402/depression-and-anxiety-data?resource=download
Number of Attributes: 19
Number of Objects: 783
Table :
| Attribute Name | Description | Data Type | Possible Values |
|---|---|---|---|
| ID | student id | Nominal | 3 values |
| school_year | student current year | Ordinal | 1-4 |
| Age | student age | Numeric | 18-24 |
| Gender | student gender | Binary | female/male |
| BMI | body mass index | Numerical | 9-50 |
| who_bmi | bmi classification | Nominal | Underweight/Normal/Overweight/Obese |
| PHQ Score | Patient Health Questionnaire | Ordinal | 0-27 |
| depression_severity | severity of depression | Nominal | Mild/Moderate/Moderately Severe/Severe/None-Minimal |
| depressiveness | depressiveness | Binary | TRUE/FALSE |
| Suicidal | likely to commit suicide | Binary | TRUE/FALSE |
| depression_diagnosis | depression diagnosis | Binary | TRUE/FALSE |
| depression_treatment | treating depression | Binary | TRUE/FALSE |
| GAD Score | Generalized Anxiety Disorder | Ordinal | 0-<15 |
| anxiety_severity | severity of anxiety | Nominal | Mild/Moderate/Moderately Severe/Severe/None-Minimal |
| anxiousness | anxiousness | Binary | TRUE/FALSE |
| anxiety_diagnosis | anxiety diagnosis | Binary | TRUE/FALSE |
| anxiety_treatment | treating of anxiety | Binary | TRUE/FALSE |
| EPWORTH Score | The Epworth Sleepiness Scale | ordinal | 0-15 |
| Sleepiness | state of being sleepy | Binary | TRUE/FALSE |
#loading the neceassary libraries
suppressWarnings({
library(dplyr)
library(readr)
library(caret)
library(tidyverse)
library(rpart)
library(rattle)
library(rpart.plot)
library(RColorBrewer)
library(FSelector)
})##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## Loading required package: ggplot2## Loading required package: lattice## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ lubridate 1.9.3 ✔ tibble 3.2.1
## ✔ purrr 1.0.2 ✔ tidyr 1.3.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
## Loading required package: bitops
##
## Rattle: A free graphical interface for data science with R.
## Version 5.5.1 Copyright (c) 2006-2021 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.dataset<-read_csv("depression_anxiety_data.csv")## Rows: 783 Columns: 19
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): gender, who_bmi, depression_severity, anxiety_severity
## dbl (7): id, school_year, age, bmi, phq_score, gad_score, epworth_score
## lgl (8): depressiveness, suicidal, depression_diagnosis, depression_treatmen...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.################################### preproccing steps
##find missing values
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## [783,] FALSE FALSE FALSE FALSE##count missing values
sum(is.na(dataset))## [1] 41#delete the missing values
dataset[dataset=="Not Availble"]<- NA
dim(dataset)## [1] 783 19dataset = na.omit(dataset)
dim(dataset)## [1] 757 19sum(is.na(dataset))## [1] 0print(dataset)## # A tibble: 757 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <dbl> <chr> <dbl> <chr>
## 1 1 1 19 male 33.3 Class I O… 9 Mild
## 2 2 1 18 male 19.8 Normal 8 Mild
## 3 3 1 19 male 25.1 Overweight 8 Mild
## 4 4 1 18 female 23.7 Normal 19 Moderately severe
## 5 5 1 18 male 25.6 Overweight 6 Mild
## 6 6 1 18 male 22.1 Normal 3 None-minimal
## 7 7 1 18 male 22.4 Normal 6 Mild
## 8 8 1 19 male 20.5 Normal 4 None-minimal
## 9 9 1 20 male 21.2 Normal 11 Moderate
## 10 10 1 19 male 24.5 Normal 6 Mild
## # ℹ 747 more rows
## # ℹ 11 more variables: depressiveness <lgl>, suicidal <lgl>,
## # depression_diagnosis <lgl>, depression_treatment <lgl>, gad_score <dbl>,
## # anxiety_severity <chr>, anxiousness <lgl>, anxiety_diagnosis <lgl>,
## # anxiety_treatment <lgl>, epworth_score <dbl>, sleepiness <lgl>i
#Detect Outliers
#install.packages("outliers")
library(outliers)Outage = outlier(dataset$age, logical =TRUE)
sum(Outage)## [1] 2Find_outlier = which(Outage ==TRUE, arr.ind = TRUE)
Outage## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSEFind_outlier## [1] 240 590#
Outbmi= outlier(dataset$bmi, logical =TRUE)
sum(Outbmi)## [1] 1Find_outlier2 = which(Outbmi==TRUE, arr.ind = TRUE)
Outbmi## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [61] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [745] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [757] FALSEFind_outlier2## [1] 64#delet outliers
dataset= dataset[-Find_outlier,]
dataset= dataset[-Find_outlier2,]# data transformation (change the TRUR and False to 0 and 1 )
dataset$depressiveness = factor (dataset$depressiveness, levels = c(TRUE,FALSE), labels=c(1,0))
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <dbl> <chr> <dbl> <chr>
## 1 1 1 19 male 33.3 Class I O… 9 Mild
## 2 2 1 18 male 19.8 Normal 8 Mild
## 3 3 1 19 male 25.1 Overweight 8 Mild
## 4 4 1 18 female 23.7 Normal 19 Moderately severe
## 5 5 1 18 male 25.6 Overweight 6 Mild
## 6 6 1 18 male 22.1 Normal 3 None-minimal
## 7 7 1 18 male 22.4 Normal 6 Mild
## 8 8 1 19 male 20.5 Normal 4 None-minimal
## 9 9 1 20 male 21.2 Normal 11 Moderate
## 10 10 1 19 male 24.5 Normal 6 Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <lgl>,
## # depression_diagnosis <lgl>, depression_treatment <lgl>, gad_score <dbl>,
## # anxiety_severity <chr>, anxiousness <lgl>, anxiety_diagnosis <lgl>,
## # anxiety_treatment <lgl>, epworth_score <dbl>, sleepiness <lgl>dataset$suicidal = factor (dataset$suicidal, levels = c(TRUE,FALSE), labels=c(1,0))
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <dbl> <chr> <dbl> <chr>
## 1 1 1 19 male 33.3 Class I O… 9 Mild
## 2 2 1 18 male 19.8 Normal 8 Mild
## 3 3 1 19 male 25.1 Overweight 8 Mild
## 4 4 1 18 female 23.7 Normal 19 Moderately severe
## 5 5 1 18 male 25.6 Overweight 6 Mild
## 6 6 1 18 male 22.1 Normal 3 None-minimal
## 7 7 1 18 male 22.4 Normal 6 Mild
## 8 8 1 19 male 20.5 Normal 4 None-minimal
## 9 9 1 20 male 21.2 Normal 11 Moderate
## 10 10 1 19 male 24.5 Normal 6 Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <fct>,
## # depression_diagnosis <lgl>, depression_treatment <lgl>, gad_score <dbl>,
## # anxiety_severity <chr>, anxiousness <lgl>, anxiety_diagnosis <lgl>,
## # anxiety_treatment <lgl>, epworth_score <dbl>, sleepiness <lgl>dataset$depression_diagnosis = factor (dataset$depression_diagnosis, levels = c(TRUE,FALSE), labels=c(1,0))
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <dbl> <chr> <dbl> <chr>
## 1 1 1 19 male 33.3 Class I O… 9 Mild
## 2 2 1 18 male 19.8 Normal 8 Mild
## 3 3 1 19 male 25.1 Overweight 8 Mild
## 4 4 1 18 female 23.7 Normal 19 Moderately severe
## 5 5 1 18 male 25.6 Overweight 6 Mild
## 6 6 1 18 male 22.1 Normal 3 None-minimal
## 7 7 1 18 male 22.4 Normal 6 Mild
## 8 8 1 19 male 20.5 Normal 4 None-minimal
## 9 9 1 20 male 21.2 Normal 11 Moderate
## 10 10 1 19 male 24.5 Normal 6 Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <fct>,
## # depression_diagnosis <fct>, depression_treatment <lgl>, gad_score <dbl>,
## # anxiety_severity <chr>, anxiousness <lgl>, anxiety_diagnosis <lgl>,
## # anxiety_treatment <lgl>, epworth_score <dbl>, sleepiness <lgl>dataset$depression_treatment = factor (dataset$depression_treatment, levels = c(TRUE,FALSE), labels=c(1,0))
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <dbl> <chr> <dbl> <chr>
## 1 1 1 19 male 33.3 Class I O… 9 Mild
## 2 2 1 18 male 19.8 Normal 8 Mild
## 3 3 1 19 male 25.1 Overweight 8 Mild
## 4 4 1 18 female 23.7 Normal 19 Moderately severe
## 5 5 1 18 male 25.6 Overweight 6 Mild
## 6 6 1 18 male 22.1 Normal 3 None-minimal
## 7 7 1 18 male 22.4 Normal 6 Mild
## 8 8 1 19 male 20.5 Normal 4 None-minimal
## 9 9 1 20 male 21.2 Normal 11 Moderate
## 10 10 1 19 male 24.5 Normal 6 Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <fct>,
## # depression_diagnosis <fct>, depression_treatment <fct>, gad_score <dbl>,
## # anxiety_severity <chr>, anxiousness <lgl>, anxiety_diagnosis <lgl>,
## # anxiety_treatment <lgl>, epworth_score <dbl>, sleepiness <lgl>dataset$anxiousness = factor (dataset$anxiousness, levels = c(TRUE,FALSE), labels=c(1,0))
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <dbl> <chr> <dbl> <chr>
## 1 1 1 19 male 33.3 Class I O… 9 Mild
## 2 2 1 18 male 19.8 Normal 8 Mild
## 3 3 1 19 male 25.1 Overweight 8 Mild
## 4 4 1 18 female 23.7 Normal 19 Moderately severe
## 5 5 1 18 male 25.6 Overweight 6 Mild
## 6 6 1 18 male 22.1 Normal 3 None-minimal
## 7 7 1 18 male 22.4 Normal 6 Mild
## 8 8 1 19 male 20.5 Normal 4 None-minimal
## 9 9 1 20 male 21.2 Normal 11 Moderate
## 10 10 1 19 male 24.5 Normal 6 Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <fct>,
## # depression_diagnosis <fct>, depression_treatment <fct>, gad_score <dbl>,
## # anxiety_severity <chr>, anxiousness <fct>, anxiety_diagnosis <lgl>,
## # anxiety_treatment <lgl>, epworth_score <dbl>, sleepiness <lgl>dataset$anxiety_diagnosis = factor (dataset$anxiety_diagnosis, levels = c(TRUE,FALSE), labels=c(1,0))
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <dbl> <chr> <dbl> <chr>
## 1 1 1 19 male 33.3 Class I O… 9 Mild
## 2 2 1 18 male 19.8 Normal 8 Mild
## 3 3 1 19 male 25.1 Overweight 8 Mild
## 4 4 1 18 female 23.7 Normal 19 Moderately severe
## 5 5 1 18 male 25.6 Overweight 6 Mild
## 6 6 1 18 male 22.1 Normal 3 None-minimal
## 7 7 1 18 male 22.4 Normal 6 Mild
## 8 8 1 19 male 20.5 Normal 4 None-minimal
## 9 9 1 20 male 21.2 Normal 11 Moderate
## 10 10 1 19 male 24.5 Normal 6 Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <fct>,
## # depression_diagnosis <fct>, depression_treatment <fct>, gad_score <dbl>,
## # anxiety_severity <chr>, anxiousness <fct>, anxiety_diagnosis <fct>,
## # anxiety_treatment <lgl>, epworth_score <dbl>, sleepiness <lgl>dataset$anxiety_treatment = factor (dataset$anxiety_treatment, levels = c(TRUE,FALSE), labels=c(1,0))
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <dbl> <chr> <dbl> <chr>
## 1 1 1 19 male 33.3 Class I O… 9 Mild
## 2 2 1 18 male 19.8 Normal 8 Mild
## 3 3 1 19 male 25.1 Overweight 8 Mild
## 4 4 1 18 female 23.7 Normal 19 Moderately severe
## 5 5 1 18 male 25.6 Overweight 6 Mild
## 6 6 1 18 male 22.1 Normal 3 None-minimal
## 7 7 1 18 male 22.4 Normal 6 Mild
## 8 8 1 19 male 20.5 Normal 4 None-minimal
## 9 9 1 20 male 21.2 Normal 11 Moderate
## 10 10 1 19 male 24.5 Normal 6 Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <fct>,
## # depression_diagnosis <fct>, depression_treatment <fct>, gad_score <dbl>,
## # anxiety_severity <chr>, anxiousness <fct>, anxiety_diagnosis <fct>,
## # anxiety_treatment <fct>, epworth_score <dbl>, sleepiness <lgl>dataset$sleepiness = factor (dataset$sleepiness, levels = c(TRUE,FALSE), labels=c(1,0))
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <dbl> <chr> <dbl> <chr>
## 1 1 1 19 male 33.3 Class I O… 9 Mild
## 2 2 1 18 male 19.8 Normal 8 Mild
## 3 3 1 19 male 25.1 Overweight 8 Mild
## 4 4 1 18 female 23.7 Normal 19 Moderately severe
## 5 5 1 18 male 25.6 Overweight 6 Mild
## 6 6 1 18 male 22.1 Normal 3 None-minimal
## 7 7 1 18 male 22.4 Normal 6 Mild
## 8 8 1 19 male 20.5 Normal 4 None-minimal
## 9 9 1 20 male 21.2 Normal 11 Moderate
## 10 10 1 19 male 24.5 Normal 6 Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <fct>,
## # depression_diagnosis <fct>, depression_treatment <fct>, gad_score <dbl>,
## # anxiety_severity <chr>, anxiousness <fct>, anxiety_diagnosis <fct>,
## # anxiety_treatment <fct>, epworth_score <dbl>, sleepiness <fct>
```r
#Discretization the values based on fixed set of predetermined criteria
#1- bmi discretizatio (indicate high body fatness)
breaks <- c(18,18.4,24.9,29.9,34.9,39.9,100)
dataset$bmi= cut(dataset$bmi, breaks = breaks)
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <fct> <chr> <dbl> <chr>
## 1 1 1 19 male (29.9,3… Class … 9 Mild
## 2 2 1 18 male (18.4,2… Normal 8 Mild
## 3 3 1 19 male (24.9,2… Overwe… 8 Mild
## 4 4 1 18 female (18.4,2… Normal 19 Moderately severe
## 5 5 1 18 male (24.9,2… Overwe… 6 Mild
## 6 6 1 18 male (18.4,2… Normal 3 None-minimal
## 7 7 1 18 male (18.4,2… Normal 6 Mild
## 8 8 1 19 male (18.4,2… Normal 4 None-minimal
## 9 9 1 20 male (18.4,2… Normal 11 Moderate
## 10 10 1 19 male (18.4,2… Normal 6 Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <fct>,
## # depression_diagnosis <fct>, depression_treatment <fct>, gad_score <dbl>,
## # anxiety_severity <chr>, anxiousness <fct>, anxiety_diagnosis <fct>,
## # anxiety_treatment <fct>, epworth_score <dbl>, sleepiness <fct>#2- phq test score discretizatio(Depression Test Questionnaire)
breaks <- c(0,4,9,14,19,27)
dataset$phq_score= cut(dataset$phq_score, breaks = breaks)
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <fct> <chr> <fct> <chr>
## 1 1 1 19 male (29.9,3… Class … (4,9] Mild
## 2 2 1 18 male (18.4,2… Normal (4,9] Mild
## 3 3 1 19 male (24.9,2… Overwe… (4,9] Mild
## 4 4 1 18 female (18.4,2… Normal (14,19] Moderately severe
## 5 5 1 18 male (24.9,2… Overwe… (4,9] Mild
## 6 6 1 18 male (18.4,2… Normal (0,4] None-minimal
## 7 7 1 18 male (18.4,2… Normal (4,9] Mild
## 8 8 1 19 male (18.4,2… Normal (0,4] None-minimal
## 9 9 1 20 male (18.4,2… Normal (9,14] Moderate
## 10 10 1 19 male (18.4,2… Normal (4,9] Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <fct>,
## # depression_diagnosis <fct>, depression_treatment <fct>, gad_score <dbl>,
## # anxiety_severity <chr>, anxiousness <fct>, anxiety_diagnosis <fct>,
## # anxiety_treatment <fct>, epworth_score <dbl>, sleepiness <fct>#3- gad test score discretization(Generalised Anxiety Disorder Assessment)
breaks <- c(0,4,9,14,21)
dataset$gad_score= cut(dataset$gad_score, breaks = breaks)
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <fct> <chr> <fct> <chr>
## 1 1 1 19 male (29.9,3… Class … (4,9] Mild
## 2 2 1 18 male (18.4,2… Normal (4,9] Mild
## 3 3 1 19 male (24.9,2… Overwe… (4,9] Mild
## 4 4 1 18 female (18.4,2… Normal (14,19] Moderately severe
## 5 5 1 18 male (24.9,2… Overwe… (4,9] Mild
## 6 6 1 18 male (18.4,2… Normal (0,4] None-minimal
## 7 7 1 18 male (18.4,2… Normal (4,9] Mild
## 8 8 1 19 male (18.4,2… Normal (0,4] None-minimal
## 9 9 1 20 male (18.4,2… Normal (9,14] Moderate
## 10 10 1 19 male (18.4,2… Normal (4,9] Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <fct>,
## # depression_diagnosis <fct>, depression_treatment <fct>, gad_score <fct>,
## # anxiety_severity <chr>, anxiousness <fct>, anxiety_diagnosis <fct>,
## # anxiety_treatment <fct>, epworth_score <dbl>, sleepiness <fct>#4- Epworth test score discretizatio (Sleepiness Scale)
breaks <- c(0,10,14,17,24)
dataset$epworth_score= cut(dataset$epworth_score, breaks = breaks)
print(dataset)## # A tibble: 754 × 19
## id school_year age gender bmi who_bmi phq_score depression_severity
## <dbl> <dbl> <dbl> <chr> <fct> <chr> <fct> <chr>
## 1 1 1 19 male (29.9,3… Class … (4,9] Mild
## 2 2 1 18 male (18.4,2… Normal (4,9] Mild
## 3 3 1 19 male (24.9,2… Overwe… (4,9] Mild
## 4 4 1 18 female (18.4,2… Normal (14,19] Moderately severe
## 5 5 1 18 male (24.9,2… Overwe… (4,9] Mild
## 6 6 1 18 male (18.4,2… Normal (0,4] None-minimal
## 7 7 1 18 male (18.4,2… Normal (4,9] Mild
## 8 8 1 19 male (18.4,2… Normal (0,4] None-minimal
## 9 9 1 20 male (18.4,2… Normal (9,14] Moderate
## 10 10 1 19 male (18.4,2… Normal (4,9] Mild
## # ℹ 744 more rows
## # ℹ 11 more variables: depressiveness <fct>, suicidal <fct>,
## # depression_diagnosis <fct>, depression_treatment <fct>, gad_score <fct>,
## # anxiety_severity <chr>, anxiousness <fct>, anxiety_diagnosis <fct>,
## # anxiety_treatment <fct>, epworth_score <fct>, sleepiness <fct>######### end of preproccing ########### diagram for the class label (depressivness)
boolean_data <- dataset$depressiveness
print(boolean_data)## [1] 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0
## [38] 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0
## [75] 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0
## [112] 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0
## [149] 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1
## [186] 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 1
## [223] 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0
## [260] 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1
## [297] 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0
## [334] 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1
## [371] 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1
## [408] 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0
## [445] 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [482] 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0
## [519] 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0
## [556] 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
## [593] 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0
## [630] 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0
## [667] 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0
## [704] 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1
## [741] 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## Levels: 1 0# Count the occurrences of TRUE and FALSE values
true_count <- sum(boolean_data==1)
print(true_count)## [1] 203false_count <- sum(boolean_data==0)
print(false_count)## [1] 551# Values for the bar chart
bar_heights <- c(true_count, false_count)
# Names for the bars
bar_names <- c("TRUE", "FALSE")
# Create a bar chart
barplot(bar_heights, names.arg = bar_names, col = c("blue", "red"),
xlab = "Boolean Values", ylab = "Count",
main = "class label (depressiveness)")
# phase 3 # Building model
# explore the dataset
str(dataset)## tibble [754 × 19] (S3: tbl_df/tbl/data.frame)
## $ id : num [1:754] 1 2 3 4 5 6 7 8 9 10 ...
## $ school_year : num [1:754] 1 1 1 1 1 1 1 1 1 1 ...
## $ age : num [1:754] 19 18 19 18 18 18 18 19 20 19 ...
## $ gender : chr [1:754] "male" "male" "male" "female" ...
## $ bmi : Factor w/ 6 levels "(18,18.4]","(18.4,24.9]",..: 4 2 3 2 3 2 2 2 2 2 ...
## $ who_bmi : chr [1:754] "Class I Obesity" "Normal" "Overweight" "Normal" ...
## $ phq_score : Factor w/ 5 levels "(0,4]","(4,9]",..: 2 2 2 4 2 1 2 1 3 2 ...
## $ depression_severity : chr [1:754] "Mild" "Mild" "Mild" "Moderately severe" ...
## $ depressiveness : Factor w/ 2 levels "1","0": 2 2 2 1 2 2 2 2 1 2 ...
## $ suicidal : Factor w/ 2 levels "1","0": 2 2 2 1 2 2 2 2 2 2 ...
## $ depression_diagnosis: Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ depression_treatment: Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ gad_score : Factor w/ 4 levels "(0,4]","(4,9]",..: 3 2 2 4 3 1 1 2 2 1 ...
## $ anxiety_severity : chr [1:754] "Moderate" "Mild" "Mild" "Severe" ...
## $ anxiousness : Factor w/ 2 levels "1","0": 1 2 2 1 1 2 2 2 2 2 ...
## $ anxiety_diagnosis : Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ anxiety_treatment : Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ epworth_score : Factor w/ 4 levels "(0,10]","(10,14]",..: 1 2 1 2 1 1 1 1 1 1 ...
## $ sleepiness : Factor w/ 2 levels "1","0": 2 1 2 1 2 2 2 2 2 2 ...
## - attr(*, "na.action")= 'omit' Named int [1:26] 12 23 24 25 30 40 51 128 158 167 ...
## ..- attr(*, "names")= chr [1:26] "12" "23" "24" "25" ...glimpse(dataset)## Rows: 754
## Columns: 19
## $ id <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16…
## $ school_year <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ age <dbl> 19, 18, 19, 18, 18, 18, 18, 19, 20, 19, 18, 19, 1…
## $ gender <chr> "male", "male", "male", "female", "male", "male",…
## $ bmi <fct> "(29.9,34.9]", "(18.4,24.9]", "(24.9,29.9]", "(18…
## $ who_bmi <chr> "Class I Obesity", "Normal", "Overweight", "Norma…
## $ phq_score <fct> "(4,9]", "(4,9]", "(4,9]", "(14,19]", "(4,9]", "(…
## $ depression_severity <chr> "Mild", "Mild", "Mild", "Moderately severe", "Mil…
## $ depressiveness <fct> 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0…
## $ suicidal <fct> 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ depression_diagnosis <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ depression_treatment <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ gad_score <fct> "(9,14]", "(4,9]", "(4,9]", "(14,21]", "(9,14]", …
## $ anxiety_severity <chr> "Moderate", "Mild", "Mild", "Severe", "Moderate",…
## $ anxiousness <fct> 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0…
## $ anxiety_diagnosis <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ anxiety_treatment <fct> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ epworth_score <fct> "(0,10]", "(10,14]", "(0,10]", "(10,14]", "(0,10]…
## $ sleepiness <fct> 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0…Check if the data is balanced or not
# Calculate class distribution
class_distribution <- dataset %>%
group_by(depressiveness) %>%
summarise(count = n()) %>%
mutate(percentage = count / sum(count) * 100)
# Print class distribution
print(class_distribution)## # A tibble: 2 × 3
## depressiveness count percentage
## <fct> <int> <dbl>
## 1 1 203 26.9
## 2 0 551 73.1barplot(prop.table(table(dataset$depressiveness)),
col = rainbow(2),
ylim = c(0, 0.7),
main = "Class Distribution")
# Based on the plot it clearly evident that 73% of the data in 0 class and the remaining 26% in another class.
# So big difference observed in the amount of data available. If we are making a model based on these a dataset accuracy predicting students not admitted will be higher compared to students who are admitted.we can observe that the dataset is imbalanced
Over Sampling to handle imbalanced
library(ROSE)## Loaded ROSE 0.0-4library(caTools)# there is still missing value
dataset <- na.omit(dataset)set.seed(123)
split <- sample.split(dataset$depressiveness, SplitRatio = 0.8)
train <- subset(dataset, split == TRUE)
test <- subset(dataset, split == FALSE)
table(train$depressiveness)##
## 1 0
## 155 386# Perform oversampling using ovun.sample
over <- ovun.sample(depressiveness ~ ., data = train, method = "over",N=772)$data
table(over$depressiveness)##
## 0 1
## 386 386actual_labels<-test$depressivenessbarplot(prop.table(table(over$depressiveness)),
col = rainbow(2),
ylim = c(0, 0.7),
main = "Class Distribution")
# as we can see the data of training is almost balanced # Perform oversampling using ovun.sample
under <- ovun.sample(depressiveness ~ ., data = train, method = "under",N=310)$data
table(under$depressiveness)##
## 0 1
## 155 155barplot(prop.table(table(under$depressiveness)),
col = rainbow(2),
ylim = c(0, 0.7),
main = "Class Distribution")
we will use over sampling for this example
Steps involved in the K-fold Cross Validation in R:
- Split the data set into K subsets randomly
- For each one of the developed subsets of data points
- treat that subset as the validation (test) set
- Use all the rest subsets for training purpose
- Training of the model and evaluate it on the validation set or test set
- Calculate prediction error
- Repeat the above step K times i.e., until the model is not trained and tested on all subsets
- Generate overall prediction error by taking the average of prediction errors in every case
let’s rename our new sampling dataset
# assign the dataset to over sample datasets
set.seed(123)
dataset<-over# make sure that the outcome column is a factor or numeric.
# we need to make sure the class lable is factor
str(dataset$depressiveness)## Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...# we can see the datatype is binary as true and false
#convert it to factor
dataset$depressiveness <- as.factor(dataset$depressiveness)DT with k-validation 5 and attribute selection information gain, gain ratio , gini index
#make data frame to track the process of the different tree
# Create an empty dataframe
evaluation_df <- data.frame(tree = character(), accuracy = numeric(),Precision = numeric(),Recall = numeric(),F1 = numeric(), Atrribute=character(),cv_K=character(),stringsAsFactors = FALSE)Spilt the data into k volds
folds <- createFolds(dataset$depressiveness, k = 5) # create the folds
# control parameters
train_control <- trainControl(method = "cv", index = folds)information gain
#build the model
tree1 <- train(depressiveness ~ ., data = dataset, trControl = train_control,
method = "rpart", parms = list(split = "information"))# train result
trained_model <- tree1$finalModel
trained_model## n= 772
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 772 386 0 (0.50000000 0.50000000)
## 2) phq_score(9,14]< 0.5 512 126 0 (0.75390625 0.24609375)
## 4) suicidal0>=0.5 421 35 0 (0.91686461 0.08313539) *
## 5) suicidal0< 0.5 91 0 1 (0.00000000 1.00000000) *
## 3) phq_score(9,14]>=0.5 260 0 1 (0.00000000 1.00000000) *#features importance
trained_model$variable.importance## depression_severityModerate phq_score(9,14]
## 249.412160 249.412160
## suicidal0 anxiety_severitySevere
## 165.139447 29.035507
## depression_severityModerately severe gad_score(14,21]
## 29.035507 29.035507
## phq_score(14,19] phq_score(19,27]
## 29.035507 27.220788
## anxiety_severityModerate gad_score(9,14]
## 8.633498 8.633498
## phq_score(4,9] bmi(39.9,100]
## 8.633498 6.714943#summary of the trainig
summary(trained_model)## Call:
## (function (formula, data, weights, subset, na.action = na.rpart,
## method, model = FALSE, x = FALSE, y = TRUE, parms, control,
## cost, ...)
## {
## Call <- match.call()
## if (is.data.frame(model)) {
## m <- model
## model <- FALSE
## }
## else {
## indx <- match(c("formula", "data", "weights", "subset"),
## names(Call), nomatch = 0)
## if (indx[1] == 0)
## stop("a 'formula' argument is required")
## temp <- Call[c(1, indx)]
## temp$na.action <- na.action
## temp[[1]] <- quote(stats::model.frame)
## m <- eval.parent(temp)
## }
## Terms <- attr(m, "terms")
## if (any(attr(Terms, "order") > 1))
## stop("Trees cannot handle interaction terms")
## Y <- model.response(m)
## wt <- model.weights(m)
## if (any(wt < 0))
## stop("negative weights not allowed")
## if (!length(wt))
## wt <- rep(1, nrow(m))
## offset <- model.offset(m)
## X <- rpart.matrix(m)
## nobs <- nrow(X)
## nvar <- ncol(X)
## if (missing(method)) {
## method <- if (is.factor(Y) || is.character(Y))
## "class"
## else if (inherits(Y, "Surv"))
## "exp"
## else if (is.matrix(Y))
## "poisson"
## else "anova"
## }
## if (is.list(method)) {
## mlist <- method
## method <- "user"
## init <- if (missing(parms))
## mlist$init(Y, offset, wt = wt)
## else mlist$init(Y, offset, parms, wt)
## keep <- rpartcallback(mlist, nobs, init)
## method.int <- 4
## parms <- init$parms
## }
## else {
## method.int <- pmatch(method, c("anova", "poisson", "class",
## "exp"))
## if (is.na(method.int))
## stop("Invalid method")
## method <- c("anova", "poisson", "class", "exp")[method.int]
## if (method.int == 4)
## method.int <- 2
## init <- if (missing(parms))
## get(paste("rpart", method, sep = "."), envir = environment())(Y,
## offset, , wt)
## else get(paste("rpart", method, sep = "."), envir = environment())(Y,
## offset, parms, wt)
## ns <- asNamespace("rpart")
## if (!is.null(init$print))
## environment(init$print) <- ns
## if (!is.null(init$summary))
## environment(init$summary) <- ns
## if (!is.null(init$text))
## environment(init$text) <- ns
## }
## Y <- init$y
## xlevels <- .getXlevels(Terms, m)
## cats <- rep(0, ncol(X))
## if (!is.null(xlevels)) {
## indx <- match(names(xlevels), colnames(X), nomatch = 0)
## cats[indx] <- (unlist(lapply(xlevels, length)))[indx >
## 0]
## }
## extraArgs <- list(...)
## if (length(extraArgs)) {
## controlargs <- names(formals(rpart.control))
## indx <- match(names(extraArgs), controlargs, nomatch = 0)
## if (any(indx == 0))
## stop(gettextf("Argument %s not matched", names(extraArgs)[indx ==
## 0]), domain = NA)
## }
## controls <- rpart.control(...)
## if (!missing(control))
## controls[names(control)] <- control
## xval <- controls$xval
## if (is.null(xval) || (length(xval) == 1 && xval == 0) ||
## method == "user") {
## xgroups <- 0
## xval <- 0
## }
## else if (length(xval) == 1) {
## xgroups <- sample(rep(1:xval, length.out = nobs), nobs,
## replace = FALSE)
## }
## else if (length(xval) == nobs) {
## xgroups <- xval
## xval <- length(unique(xgroups))
## }
## else {
## if (!is.null(attr(m, "na.action"))) {
## temp <- as.integer(attr(m, "na.action"))
## xval <- xval[-temp]
## if (length(xval) == nobs) {
## xgroups <- xval
## xval <- length(unique(xgroups))
## }
## else stop("Wrong length for 'xval'")
## }
## else stop("Wrong length for 'xval'")
## }
## if (missing(cost))
## cost <- rep(1, nvar)
## else {
## if (length(cost) != nvar)
## stop("Cost vector is the wrong length")
## if (any(cost <= 0))
## stop("Cost vector must be positive")
## }
## tfun <- function(x) if (is.matrix(x))
## rep(is.ordered(x), ncol(x))
## else is.ordered(x)
## labs <- sub("^`(.*)`$", "\\1", attr(Terms, "term.labels"))
## isord <- unlist(lapply(m[labs], tfun))
## storage.mode(X) <- "double"
## storage.mode(wt) <- "double"
## temp <- as.double(unlist(init$parms))
## if (!length(temp))
## temp <- 0
## rpfit <- .Call(C_rpart, ncat = as.integer(cats * !isord),
## method = as.integer(method.int), as.double(unlist(controls)),
## temp, as.integer(xval), as.integer(xgroups), as.double(t(init$y)),
## X, wt, as.integer(init$numy), as.double(cost))
## nsplit <- nrow(rpfit$isplit)
## ncat <- if (!is.null(rpfit$csplit))
## nrow(rpfit$csplit)
## else 0
## if (nsplit == 0)
## xval <- 0
## numcp <- ncol(rpfit$cptable)
## temp <- if (nrow(rpfit$cptable) == 3)
## c("CP", "nsplit", "rel error")
## else c("CP", "nsplit", "rel error", "xerror", "xstd")
## dimnames(rpfit$cptable) <- list(temp, 1:numcp)
## tname <- c("<leaf>", colnames(X))
## splits <- matrix(c(rpfit$isplit[, 2:3], rpfit$dsplit), ncol = 5,
## dimnames = list(tname[rpfit$isplit[, 1] + 1], c("count",
## "ncat", "improve", "index", "adj")))
## index <- rpfit$inode[, 2]
## nadd <- sum(isord[rpfit$isplit[, 1]])
## if (nadd > 0) {
## newc <- matrix(0, nadd, max(cats))
## cvar <- rpfit$isplit[, 1]
## indx <- isord[cvar]
## cdir <- splits[indx, 2]
## ccut <- floor(splits[indx, 4])
## splits[indx, 2] <- cats[cvar[indx]]
## splits[indx, 4] <- ncat + 1:nadd
## for (i in 1:nadd) {
## newc[i, 1:(cats[(cvar[indx])[i]])] <- -as.integer(cdir[i])
## newc[i, 1:ccut[i]] <- as.integer(cdir[i])
## }
## catmat <- if (ncat == 0)
## newc
## else {
## cs <- rpfit$csplit
## ncs <- ncol(cs)
## ncc <- ncol(newc)
## if (ncs < ncc)
## cs <- cbind(cs, matrix(0, nrow(cs), ncc - ncs))
## rbind(cs, newc)
## }
## ncat <- ncat + nadd
## }
## else catmat <- rpfit$csplit
## if (nsplit == 0) {
## frame <- data.frame(row.names = 1, var = "<leaf>", n = rpfit$inode[,
## 5], wt = rpfit$dnode[, 3], dev = rpfit$dnode[, 1],
## yval = rpfit$dnode[, 4], complexity = rpfit$dnode[,
## 2], ncompete = 0, nsurrogate = 0)
## }
## else {
## temp <- ifelse(index == 0, 1, index)
## svar <- ifelse(index == 0, 0, rpfit$isplit[temp, 1])
## frame <- data.frame(row.names = rpfit$inode[, 1], var = tname[svar +
## 1], n = rpfit$inode[, 5], wt = rpfit$dnode[, 3],
## dev = rpfit$dnode[, 1], yval = rpfit$dnode[, 4],
## complexity = rpfit$dnode[, 2], ncompete = pmax(0,
## rpfit$inode[, 3] - 1), nsurrogate = rpfit$inode[,
## 4])
## }
## if (method.int == 3) {
## numclass <- init$numresp - 2
## nodeprob <- rpfit$dnode[, numclass + 5]/sum(wt)
## temp <- pmax(1, init$counts)
## temp <- rpfit$dnode[, 4 + (1:numclass)] %*% diag(init$parms$prior/temp)
## yprob <- temp/rowSums(temp)
## yval2 <- matrix(rpfit$dnode[, 4 + (0:numclass)], ncol = numclass +
## 1)
## frame$yval2 <- cbind(yval2, yprob, nodeprob)
## }
## else if (init$numresp > 1)
## frame$yval2 <- rpfit$dnode[, -(1:3), drop = FALSE]
## if (is.null(init$summary))
## stop("Initialization routine is missing the 'summary' function")
## functions <- if (is.null(init$print))
## list(summary = init$summary)
## else list(summary = init$summary, print = init$print)
## if (!is.null(init$text))
## functions <- c(functions, list(text = init$text))
## if (method == "user")
## functions <- c(functions, mlist)
## where <- rpfit$which
## names(where) <- row.names(m)
## ans <- list(frame = frame, where = where, call = Call, terms = Terms,
## cptable = t(rpfit$cptable), method = method, parms = init$parms,
## control = controls, functions = functions, numresp = init$numresp)
## if (nsplit)
## ans$splits = splits
## if (ncat > 0)
## ans$csplit <- catmat + 2
## if (nsplit)
## ans$variable.importance <- importance(ans)
## if (model) {
## ans$model <- m
## if (missing(y))
## y <- FALSE
## }
## if (y)
## ans$y <- Y
## if (x) {
## ans$x <- X
## ans$wt <- wt
## }
## ans$ordered <- isord
## if (!is.null(attr(m, "na.action")))
## ans$na.action <- attr(m, "na.action")
## if (!is.null(xlevels))
## attr(ans, "xlevels") <- xlevels
## if (method == "class")
## attr(ans, "ylevels") <- init$ylevels
## class(ans) <- "rpart"
## ans
## })(formula = .outcome ~ ., data = list(c(1, 3, 7, 8, 11, 13,
## 16, 17, 18, 20, 22, 26, 27, 34, 36, 39, 41, 42, 43, 44, 46, 50,
## 53, 55, 57, 59, 60, 61, 64, 65, 67, 69, 72, 74, 78, 79, 80, 82,
## 83, 85, 86, 88, 89, 93, 95, 96, 97, 98, 100, 103, 107, 108, 109,
## 111, 112, 113, 115, 118, 119, 120, 121, 122, 123, 124, 127, 134,
## 144, 145, 149, 150, 151, 153, 157, 160, 162, 163, 164, 166, 170,
## 171, 173, 181, 182, 183, 185, 186, 192, 193, 195, 199, 200, 201,
## 204, 208, 210, 211, 213, 214, 216, 218, 220, 224, 225, 226, 228,
## 234, 240, 243, 244, 246, 248, 250, 251, 253, 254, 257, 258, 259,
## 260, 263, 265, 267, 268, 269, 270, 271, 272, 273, 274, 277, 278,
## 279, 280, 281, 282, 283, 286, 287, 293, 295, 297, 301, 306, 310,
## 311, 314, 315, 319, 322, 328, 330, 333, 337, 338, 339, 340, 341,
## 343, 348, 350, 353, 356, 357, 358, 359, 360, 361, 362, 366, 368,
## 369, 370, 371, 374, 377, 379, 380, 381, 384, 385, 387, 392, 394,
## 396, 397, 398, 400, 401, 404, 409, 410, 411, 412, 413, 414, 416,
## 419, 420, 424, 425, 426, 428, 429, 431, 432, 433, 438, 442, 443,
## 444, 448, 453, 454, 457, 458, 459, 460, 461, 463, 465, 466, 467,
## 469, 470, 471, 473, 477, 478, 479, 480, 482, 484, 486, 488, 490,
## 493, 494, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 507,
## 511, 512, 514, 515, 520, 522, 529, 532, 533, 536, 538, 540, 543,
## 546, 547, 548, 553, 555, 557, 558, 559, 561, 562, 563, 565, 567,
## 568, 570, 573, 574, 576, 578, 581, 584, 586, 587, 588, 591, 592,
## 596, 597, 599, 600, 602, 604, 605, 606, 608, 610, 611, 615, 616,
## 617, 619, 620, 621, 622, 623, 627, 628, 629, 632, 637, 639, 640,
## 642, 644, 647, 650, 651, 656, 658, 659, 660, 661, 663, 664, 667,
## 668, 673, 674, 675, 676, 678, 679, 680, 683, 684, 687, 688, 692,
## 693, 694, 696, 701, 705, 707, 708, 712, 714, 716, 719, 720, 722,
## 724, 728, 732, 733, 734, 735, 736, 737, 738, 741, 742, 743, 747,
## 750, 751, 755, 756, 757, 758, 759, 762, 764, 765, 768, 771, 772,
## 773, 774, 775, 776, 777, 778, 779, 781, 207, 646, 148, 289, 276,
## 114, 320, 761, 422, 740, 612, 363, 485, 203, 131, 261, 749, 99,
## 130, 197, 682, 323, 290, 177, 140, 364, 455, 695, 506, 455, 189,
## 682, 643, 327, 572, 320, 709, 307, 633, 189, 66, 233, 290, 15,
## 288, 681, 142, 114, 624, 327, 58, 197, 317, 135, 388, 715, 695,
## 421, 633, 77, 66, 304, 91, 346, 364, 603, 670, 304, 31, 331,
## 66, 290, 485, 641, 90, 670, 686, 549, 203, 276, 110, 446, 643,
## 292, 383, 603, 316, 662, 110, 154, 262, 749, 209, 354, 294, 276,
## 317, 15, 572, 101, 31, 476, 521, 364, 572, 307, 582, 76, 323,
## 239, 476, 91, 485, 376, 155, 646, 58, 292, 582, 236, 451, 131,
## 292, 290, 76, 312, 405, 662, 367, 376, 76, 312, 146, 312, 256,
## 131, 154, 73, 276, 307, 191, 681, 99, 641, 506, 645, 323, 521,
## 289, 302, 513, 256, 68, 130, 135, 718, 524, 405, 116, 575, 207,
## 474, 31, 304, 239, 221, 624, 700, 316, 261, 354, 312, 583, 534,
## 449, 446, 245, 87, 66, 15, 612, 56, 364, 99, 318, 307, 455, 99,
## 304, 238, 624, 110, 91, 717, 782, 148, 221, 101, 730, 388, 191,
## 312, 236, 266, 309, 346, 238, 534, 101, 485, 196, 402, 116, 142,
## 582, 347, 130, 191, 345, 264, 276, 318, 481, 726, 73, 449, 346,
## 15, 624, 625, 524, 45, 450, 782, 749, 646, 718, 464, 245, 681,
## 152, 146, 101, 203, 68, 323, 723, 681, 682, 288, 68, 449, 135,
## 645, 700, 188, 730, 700, 101, 717, 402, 290, 513, 405, 633, 177,
## 749, 323, 367, 142, 583, 761, 191, 769, 196, 66, 721, 177, 423,
## 288, 421, 245, 239, 129, 723, 449, 717, 575, 276, 131, 66, 730,
## 582, 312, 363, 99, 686, 721, 233, 449, 154, 136, 87, 155, 761,
## 140, 196, 237, 761, 142, 730, 405, 87, 549, 45, 239, 318, 402,
## 307, 630, 760, 316, 364, 421, 207, 91, 288, 73, 363, 191, 450,
## 135, 421, 159, 641, 138, 154, 364, 317, 154, 304, 513, 152, 625,
## 206, 643, 73, 177, 485, 670, 464, 327, 383, 721, 15, 320, 143,
## 302, 545, 207, 695, 140, 290, 643, 196, 545, 715, 534, 323, 318,
## 421, 575, 726, 485, 464, 136, 155, 239, 241, 28, 76, 227, 92,
## 521, 76, 423), c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3,
## 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
## 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
## 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
## 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
## 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
## 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
## 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
## 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 1, 2, 2, 1, 2,
## 4, 2, 4, 4, 2, 3, 1, 1, 1, 4, 1, 1, 1, 4, 2, 2, 1, 1, 2, 2, 4,
## 3, 2, 1, 4, 4, 2, 3, 2, 4, 2, 4, 1, 1, 1, 2, 1, 2, 4, 1, 1, 4,
## 2, 1, 1, 2, 1, 2, 4, 4, 2, 4, 1, 1, 2, 1, 2, 2, 3, 4, 2, 1, 2,
## 1, 2, 3, 4, 1, 4, 4, 3, 1, 2, 1, 2, 4, 2, 2, 3, 2, 4, 1, 1, 1,
## 4, 1, 2, 2, 2, 2, 1, 3, 1, 1, 3, 3, 2, 3, 2, 3, 1, 2, 1, 3, 1,
## 3, 2, 1, 4, 1, 2, 3, 1, 2, 1, 2, 2, 1, 2, 2, 4, 2, 2, 1, 2, 1,
## 2, 1, 1, 1, 1, 2, 2, 1, 4, 1, 4, 3, 4, 2, 3, 2, 2, 3, 1, 1, 1,
## 1, 4, 3, 2, 1, 3, 1, 3, 1, 2, 1, 1, 4, 4, 2, 1, 2, 2, 3, 3, 2,
## 2, 1, 1, 1, 1, 4, 1, 2, 1, 2, 2, 2, 1, 2, 1, 4, 1, 1, 4, 4, 1,
## 1, 1, 4, 2, 1, 2, 1, 1, 2, 2, 1, 3, 1, 3, 1, 2, 1, 1, 3, 2, 1,
## 1, 2, 1, 2, 2, 3, 4, 1, 2, 2, 1, 4, 4, 3, 1, 2, 4, 4, 4, 4, 2,
## 1, 4, 1, 1, 1, 1, 1, 2, 4, 4, 4, 2, 1, 2, 1, 4, 4, 1, 4, 4, 1,
## 4, 2, 2, 3, 2, 4, 1, 4, 2, 2, 1, 3, 4, 1, 4, 1, 1, 4, 1, 2, 2,
## 2, 1, 1, 1, 4, 2, 4, 3, 2, 1, 1, 4, 3, 2, 2, 1, 4, 4, 1, 2, 1,
## 1, 1, 1, 4, 1, 1, 1, 4, 1, 4, 2, 1, 3, 1, 1, 2, 2, 2, 4, 4, 2,
## 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 2, 2, 1, 2, 3, 1,
## 4, 1, 4, 1, 1, 3, 4, 2, 2, 2, 4, 1, 2, 1, 2, 3, 1, 4, 1, 2, 4,
## 1, 3, 4, 3, 2, 2, 2, 3, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1,
## 2), c(19, 19, 18, 19, 18, 19, 18, 18, 18, 18, 18, 18, 19, 19,
## 18, 19, 19, 18, 19, 19, 18, 18, 18, 18, 19, 19, 19, 19, 19, 18,
## 18, 24, 19, 18, 19, 20, 20, 18, 18, 20, 18, 18, 18, 19, 20, 19,
## 18, 18, 18, 18, 19, 18, 19, 18, 18, 18, 18, 18, 18, 18, 18, 18,
## 18, 18, 19, 18, 18, 18, 19, 18, 20, 19, 18, 18, 18, 18, 20, 19,
## 19, 18, 18, 20, 18, 18, 18, 19, 26, 20, 20, 19, 19, 23, 19, 19,
## 20, 19, 20, 20, 24, 20, 20, 19, 19, 18, 19, 19, 20, 19, 19, 19,
## 19, 19, 19, 20, 20, 19, 20, 19, 20, 19, 19, 20, 19, 20, 24, 22,
## 19, 20, 21, 20, 21, 19, 21, 20, 25, 19, 19, 20, 20, 20, 19, 20,
## 19, 19, 18, 19, 19, 20, 19, 19, 23, 18, 19, 19, 19, 20, 19, 20,
## 19, 22, 19, 19, 19, 21, 22, 19, 20, 18, 20, 19, 19, 21, 19, 21,
## 20, 19, 19, 20, 22, 19, 19, 19, 20, 19, 20, 19, 20, 20, 20, 19,
## 23, 19, 19, 20, 20, 19, 21, 20, 19, 21, 19, 19, 20, 20, 19, 20,
## 19, 23, 19, 19, 20, 20, 19, 19, 25, 20, 21, 19, 20, 20, 19, 20,
## 20, 21, 20, 20, 20, 20, 21, 22, 20, 20, 21, 26, 20, 20, 20, 21,
## 20, 20, 20, 20, 20, 21, 20, 21, 20, 20, 21, 20, 22, 23, 19, 21,
## 22, 21, 20, 21, 20, 20, 21, 22, 20, 22, 21, 23, 22, 21, 21, 21,
## 21, 21, 21, 22, 21, 23, 21, 22, 21, 18, 21, 25, 22, 21, 21, 21,
## 21, 21, 20, 27, 21, 22, 22, 23, 21, 23, 22, 21, 22, 21, 21, 21,
## 21, 21, 21, 21, 21, 21, 21, 22, 22, 24, 22, 22, 24, 21, 22, 21,
## 22, 25, 21, 24, 22, 21, 21, 21, 21, 22, 26, 21, 21, 21, 21, 21,
## 22, 22, 22, 22, 21, 21, 21, 20, 21, 21, 21, 21, 21, 21, 22, 22,
## 21, 21, 23, 21, 22, 22, 22, 22, 26, 22, 22, 22, 22, 30, 22, 23,
## 24, 22, 23, 22, 22, 24, 22, 23, 24, 23, 21, 22, 23, 22, 23, 22,
## 23, 22, 24, 22, 18, 21, 18, 20, 19, 18, 24, 22, 19, 21, 24, 20,
## 20, 19, 18, 19, 22, 19, 18, 20, 21, 19, 20, 18, 18, 19, 20, 21,
## 28, 20, 21, 21, 21, 22, 22, 24, 21, 19, 22, 21, 18, 19, 20, 18,
## 23, 22, 19, 18, 21, 22, 18, 20, 20, 20, 20, 21, 21, 19, 22, 19,
## 18, 20, 19, 19, 19, 22, 22, 20, 20, 19, 18, 20, 20, 21, 18, 22,
## 21, 20, 19, 19, 19, 19, 21, 19, 18, 22, 19, 22, 19, 19, 19, 22,
## 21, 22, 20, 19, 20, 18, 22, 19, 20, 20, 22, 19, 22, 19, 22, 20,
## 19, 22, 20, 19, 20, 19, 18, 21, 18, 19, 22, 19, 19, 18, 19, 20,
## 20, 19, 19, 22, 19, 19, 20, 19, 23, 19, 21, 18, 19, 20, 19, 19,
## 20, 22, 19, 21, 28, 21, 19, 22, 20, 19, 21, 21, 20, 18, 20, 21,
## 21, 19, 18, 22, 18, 20, 20, 20, 22, 21, 21, 22, 19, 19, 22, 19,
## 22, 20, 20, 19, 19, 19, 18, 18, 24, 19, 19, 19, 19, 19, 20, 19,
## 20, 21, 21, 19, 19, 21, 22, 18, 21, 19, 22, 20, 20, 19, 19, 21,
## 19, 19, 21, 20, 19, 20, 19, 19, 18, 19, 22, 19, 18, 20, 21, 19,
## 19, 19, 20, 21, 20, 20, 19, 18, 21, 21, 21, 18, 19, 22, 22, 21,
## 21, 19, 19, 22, 18, 23, 19, 19, 20, 19, 21, 22, 21, 23, 20, 20,
## 20, 21, 22, 23, 22, 22, 19, 21, 19, 20, 21, 19, 22, 18, 22, 19,
## 19, 19, 22, 22, 20, 22, 19, 18, 21, 18, 19, 23, 19, 19, 22, 19,
## 21, 20, 21, 22, 19, 18, 18, 22, 22, 19, 20, 19, 21, 21, 19, 20,
## 19, 21, 19, 18, 22, 18, 19, 23, 22, 19, 22, 19, 19, 20, 18, 22,
## 19, 19, 19, 21, 22, 19, 19, 19, 18, 19, 23, 20, 20, 20, 19, 20,
## 19, 20, 21, 19, 19, 19, 20, 19, 20, 21, 18, 21, 20, 21, 20, 18,
## 20, 22, 19, 22, 18, 21, 18, 24, 19, 19, 21, 18, 21, 18, 20, 21,
## 19, 21, 21, 20, 19, 19, 19, 22, 21, 20, 19, 21, 18, 22, 20, 18,
## 20, 24, 18, 22, 20, 19), c(1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1,
## 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1,
## 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1,
## 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0,
## 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1,
## 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1,
## 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0,
## 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1,
## 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0,
## 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0,
## 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1,
## 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0,
## 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1,
## 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0,
## 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1,
## 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1,
## 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0,
## 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,
## 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0,
## 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0,
## 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1,
## 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0,
## 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1,
## 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0,
## 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0,
## 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0,
## 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1,
## 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1,
## 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0,
## 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0,
## 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1,
## 0, 1, 1, 1), c(0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1,
## 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0,
## 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1,
## 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0,
## 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0,
## 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1,
## 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0,
## 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1,
## 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0,
## 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0,
## 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1,
## 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1,
## 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0,
## 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1,
## 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1,
## 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0,
## 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0,
## 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0,
## 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1
## ), c(0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1,
## 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
## 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0,
## 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0,
## 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0,
## 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0,
## 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1,
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## 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1,
## 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0,
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## 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1,
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## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0), c(1, 0,
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## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0),
## c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1,
## 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1,
## 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1,
## 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1,
## 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0,
## 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0,
## 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1,
## 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1,
## 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0,
## 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1,
## 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1,
## 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0,
## 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1,
## 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1,
## 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1), c(1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1,
## 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1,
## 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 1), c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1,
## 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1),
## c(0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
## 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0,
## 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0,
## 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1,
## 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0,
## 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1,
## 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1,
## 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1,
## 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
## 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1,
## 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0,
## 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1,
## 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0,
## 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1,
## 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1,
## 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1,
## 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0,
## 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1,
## 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,
## 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
## 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1,
## 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0,
## 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1,
## 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1,
## 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1,
## 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1,
## 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0,
## 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1,
## 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1), c(1, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1,
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## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1,
## 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1,
## 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0,
## 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0,
## 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1,
## 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,
## 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1,
## 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1,
## 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1,
## 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0,
## 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1,
## 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1,
## 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1,
## 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1,
## 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1,
## 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0,
## 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1,
## 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1), c(1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1,
## 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0,
## 1, 1, 1, 0, 1, 1), c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0,
## 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1,
## 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1,
## 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1),
## c(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0,
## 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0,
## 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1,
## 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), c(0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0), c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0),
## c(1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1,
## 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1,
## 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1,
## 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0,
## 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1,
## 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1,
## 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0,
## 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0,
## 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1,
## 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0,
## 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1,
## 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1), c(1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2)), parms = list("information"), control = list(
## 20, 7, 0, 4, 5, 2, 0, 30, 0))
## n= 772
##
## CP nsplit rel error
## 1 0.67357513 0 1.00000000
## 2 0.23575130 1 0.32642487
## 3 0.08290155 2 0.09067358
##
## Variable importance
## depression_severityModerate phq_score(9,14]
## 30 30
## suicidal0 anxiety_severitySevere
## 20 3
## depression_severityModerately severe gad_score(14,21]
## 3 3
## phq_score(14,19] phq_score(19,27]
## 3 3
## anxiety_severityModerate gad_score(9,14]
## 1 1
## phq_score(4,9] bmi(39.9,100]
## 1 1
##
## Node number 1: 772 observations, complexity param=0.6735751
## predicted class=0 expected loss=0.5 P(node) =1
## class counts: 386 386
## probabilities: 0.500 0.500
## left son=2 (512 obs) right son=3 (260 obs)
## Primary splits:
## phq_score(9,14] < 0.5 to the left, improve=249.4122, (0 missing)
## depression_severityModerate < 0.5 to the left, improve=249.4122, (0 missing)
## phq_score(4,9] < 0.5 to the right, improve=143.4014, (0 missing)
## depression_severityNone-minimal < 0.5 to the right, improve=122.2384, (0 missing)
## suicidal0 < 0.5 to the right, improve=111.7340, (0 missing)
## Surrogate splits:
## depression_severityModerate < 0.5 to the left, agree=1.000, adj=1.000, (0 split)
## phq_score(4,9] < 0.5 to the right, agree=0.675, adj=0.035, (0 split)
## gad_score(9,14] < 0.5 to the left, agree=0.675, adj=0.035, (0 split)
## anxiety_severityModerate < 0.5 to the left, agree=0.675, adj=0.035, (0 split)
## bmi(39.9,100] < 0.5 to the left, agree=0.672, adj=0.027, (0 split)
##
## Node number 2: 512 observations, complexity param=0.2357513
## predicted class=0 expected loss=0.2460938 P(node) =0.6632124
## class counts: 386 126
## probabilities: 0.754 0.246
## left son=4 (421 obs) right son=5 (91 obs)
## Primary splits:
## suicidal0 < 0.5 to the right, improve=165.13940, (0 missing)
## phq_score(14,19] < 0.5 to the left, improve=139.20830, (0 missing)
## depression_severityModerately severe < 0.5 to the left, improve=139.20830, (0 missing)
## anxiousness0 < 0.5 to the right, improve= 71.60343, (0 missing)
## gad_score(14,21] < 0.5 to the left, improve= 63.80621, (0 missing)
## Surrogate splits:
## phq_score(14,19] < 0.5 to the left, agree=0.854, adj=0.176, (0 split)
## depression_severityModerately severe < 0.5 to the left, agree=0.854, adj=0.176, (0 split)
## gad_score(14,21] < 0.5 to the left, agree=0.854, adj=0.176, (0 split)
## anxiety_severitySevere < 0.5 to the left, agree=0.854, adj=0.176, (0 split)
## phq_score(19,27] < 0.5 to the left, agree=0.852, adj=0.165, (0 split)
##
## Node number 3: 260 observations
## predicted class=1 expected loss=0 P(node) =0.3367876
## class counts: 0 260
## probabilities: 0.000 1.000
##
## Node number 4: 421 observations
## predicted class=0 expected loss=0.08313539 P(node) =0.5453368
## class counts: 386 35
## probabilities: 0.917 0.083
##
## Node number 5: 91 observations
## predicted class=1 expected loss=0 P(node) =0.1178756
## class counts: 0 91
## probabilities: 0.000 1.000#accuracy of the tree
accuracy <- tree1$results$Accuracy
print(paste("Accuracy:", accuracy))## [1] "Accuracy: 0.987051869102506" "Accuracy: 0.904784608686986"
## [3] "Accuracy: 0.699135602377093"# get the average accuracy across all fold
accuracy <- mean(tree1$results$Accuracy)
print(paste("Average Accuracy:", accuracy))## [1] "Average Accuracy: 0.863657360055528"predictions <- predict(tree1, test)
length(predictions)## [1] 136length(test$depressiveness)## [1] 136# predict on test data
predictions <- predict(tree1, newdata=test)
predictions <- factor(predictions, levels = levels(test$depressiveness))
# Proceed with creating the confusion matrix and calculating metrics
confusion <- confusionMatrix(predictions, test$depressiveness)
# Getting the accuracy from the confusion matrix
accuracy <- confusion$overall['Accuracy']
# Calculate precision
precision <- confusion$byClass["Precision"]
# Calculate recall (sensitivity)
recall <- confusion$byClass["Recall"]
# Calculate F1 score
f1_score <- confusion$byClass["F1"]
# Print the results
print(confusion)## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 0
## 1 35 0
## 0 4 97
##
## Accuracy : 0.9706
## 95% CI : (0.9264, 0.9919)
## No Information Rate : 0.7132
## P-Value [Acc > NIR] : 4.212e-15
##
## Kappa : 0.9258
##
## Mcnemar's Test P-Value : 0.1336
##
## Sensitivity : 0.8974
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9604
## Prevalence : 0.2868
## Detection Rate : 0.2574
## Detection Prevalence : 0.2574
## Balanced Accuracy : 0.9487
##
## 'Positive' Class : 1
## # add to the dataset of evalution
tree1 <- valuation_df <- data.frame(tree = "tree1", accuracy = accuracy,Precision =precision,Recall =recall ,F1=f1_score, Atrribute="information gain",
cv_K=5)
evaluation_df <- rbind(evaluation_df, tree1)
# visulize the tree'
fancyRpartPlot(trained_model, caption = NULL)
Gini index
dataset<-over
folds <- createFolds(dataset$depressiveness, k = 5) # create the folds
# control parameters
train_control <- trainControl(method = "cv", index = folds)#build the model
tree <- train(depressiveness ~ ., data = dataset, trControl = train_control,
method = "rpart")# train result
trained_model <- tree$finalModel
trained_model## n= 772
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 772 386 0 (0.50000000 0.50000000)
## 2) phq_score(9,14]< 0.5 512 126 0 (0.75390625 0.24609375)
## 4) suicidal0>=0.5 421 35 0 (0.91686461 0.08313539) *
## 5) suicidal0< 0.5 91 0 1 (0.00000000 1.00000000) *
## 3) phq_score(9,14]>=0.5 260 0 1 (0.00000000 1.00000000) *trained_model$variable.importance## depression_severityModerate phq_score(9,14]
## 196.015625 196.015625
## suicidal0 anxiety_severitySevere
## 125.803852 22.119359
## depression_severityModerately severe gad_score(14,21]
## 22.119359 22.119359
## phq_score(14,19] phq_score(19,27]
## 22.119359 20.736899
## anxiety_severityModerate gad_score(9,14]
## 6.785156 6.785156
## phq_score(4,9] bmi(39.9,100]
## 6.785156 5.277344#summary of the trainig
summary(trained_model)## Call:
## (function (formula, data, weights, subset, na.action = na.rpart,
## method, model = FALSE, x = FALSE, y = TRUE, parms, control,
## cost, ...)
## {
## Call <- match.call()
## if (is.data.frame(model)) {
## m <- model
## model <- FALSE
## }
## else {
## indx <- match(c("formula", "data", "weights", "subset"),
## names(Call), nomatch = 0)
## if (indx[1] == 0)
## stop("a 'formula' argument is required")
## temp <- Call[c(1, indx)]
## temp$na.action <- na.action
## temp[[1]] <- quote(stats::model.frame)
## m <- eval.parent(temp)
## }
## Terms <- attr(m, "terms")
## if (any(attr(Terms, "order") > 1))
## stop("Trees cannot handle interaction terms")
## Y <- model.response(m)
## wt <- model.weights(m)
## if (any(wt < 0))
## stop("negative weights not allowed")
## if (!length(wt))
## wt <- rep(1, nrow(m))
## offset <- model.offset(m)
## X <- rpart.matrix(m)
## nobs <- nrow(X)
## nvar <- ncol(X)
## if (missing(method)) {
## method <- if (is.factor(Y) || is.character(Y))
## "class"
## else if (inherits(Y, "Surv"))
## "exp"
## else if (is.matrix(Y))
## "poisson"
## else "anova"
## }
## if (is.list(method)) {
## mlist <- method
## method <- "user"
## init <- if (missing(parms))
## mlist$init(Y, offset, wt = wt)
## else mlist$init(Y, offset, parms, wt)
## keep <- rpartcallback(mlist, nobs, init)
## method.int <- 4
## parms <- init$parms
## }
## else {
## method.int <- pmatch(method, c("anova", "poisson", "class",
## "exp"))
## if (is.na(method.int))
## stop("Invalid method")
## method <- c("anova", "poisson", "class", "exp")[method.int]
## if (method.int == 4)
## method.int <- 2
## init <- if (missing(parms))
## get(paste("rpart", method, sep = "."), envir = environment())(Y,
## offset, , wt)
## else get(paste("rpart", method, sep = "."), envir = environment())(Y,
## offset, parms, wt)
## ns <- asNamespace("rpart")
## if (!is.null(init$print))
## environment(init$print) <- ns
## if (!is.null(init$summary))
## environment(init$summary) <- ns
## if (!is.null(init$text))
## environment(init$text) <- ns
## }
## Y <- init$y
## xlevels <- .getXlevels(Terms, m)
## cats <- rep(0, ncol(X))
## if (!is.null(xlevels)) {
## indx <- match(names(xlevels), colnames(X), nomatch = 0)
## cats[indx] <- (unlist(lapply(xlevels, length)))[indx >
## 0]
## }
## extraArgs <- list(...)
## if (length(extraArgs)) {
## controlargs <- names(formals(rpart.control))
## indx <- match(names(extraArgs), controlargs, nomatch = 0)
## if (any(indx == 0))
## stop(gettextf("Argument %s not matched", names(extraArgs)[indx ==
## 0]), domain = NA)
## }
## controls <- rpart.control(...)
## if (!missing(control))
## controls[names(control)] <- control
## xval <- controls$xval
## if (is.null(xval) || (length(xval) == 1 && xval == 0) ||
## method == "user") {
## xgroups <- 0
## xval <- 0
## }
## else if (length(xval) == 1) {
## xgroups <- sample(rep(1:xval, length.out = nobs), nobs,
## replace = FALSE)
## }
## else if (length(xval) == nobs) {
## xgroups <- xval
## xval <- length(unique(xgroups))
## }
## else {
## if (!is.null(attr(m, "na.action"))) {
## temp <- as.integer(attr(m, "na.action"))
## xval <- xval[-temp]
## if (length(xval) == nobs) {
## xgroups <- xval
## xval <- length(unique(xgroups))
## }
## else stop("Wrong length for 'xval'")
## }
## else stop("Wrong length for 'xval'")
## }
## if (missing(cost))
## cost <- rep(1, nvar)
## else {
## if (length(cost) != nvar)
## stop("Cost vector is the wrong length")
## if (any(cost <= 0))
## stop("Cost vector must be positive")
## }
## tfun <- function(x) if (is.matrix(x))
## rep(is.ordered(x), ncol(x))
## else is.ordered(x)
## labs <- sub("^`(.*)`$", "\\1", attr(Terms, "term.labels"))
## isord <- unlist(lapply(m[labs], tfun))
## storage.mode(X) <- "double"
## storage.mode(wt) <- "double"
## temp <- as.double(unlist(init$parms))
## if (!length(temp))
## temp <- 0
## rpfit <- .Call(C_rpart, ncat = as.integer(cats * !isord),
## method = as.integer(method.int), as.double(unlist(controls)),
## temp, as.integer(xval), as.integer(xgroups), as.double(t(init$y)),
## X, wt, as.integer(init$numy), as.double(cost))
## nsplit <- nrow(rpfit$isplit)
## ncat <- if (!is.null(rpfit$csplit))
## nrow(rpfit$csplit)
## else 0
## if (nsplit == 0)
## xval <- 0
## numcp <- ncol(rpfit$cptable)
## temp <- if (nrow(rpfit$cptable) == 3)
## c("CP", "nsplit", "rel error")
## else c("CP", "nsplit", "rel error", "xerror", "xstd")
## dimnames(rpfit$cptable) <- list(temp, 1:numcp)
## tname <- c("<leaf>", colnames(X))
## splits <- matrix(c(rpfit$isplit[, 2:3], rpfit$dsplit), ncol = 5,
## dimnames = list(tname[rpfit$isplit[, 1] + 1], c("count",
## "ncat", "improve", "index", "adj")))
## index <- rpfit$inode[, 2]
## nadd <- sum(isord[rpfit$isplit[, 1]])
## if (nadd > 0) {
## newc <- matrix(0, nadd, max(cats))
## cvar <- rpfit$isplit[, 1]
## indx <- isord[cvar]
## cdir <- splits[indx, 2]
## ccut <- floor(splits[indx, 4])
## splits[indx, 2] <- cats[cvar[indx]]
## splits[indx, 4] <- ncat + 1:nadd
## for (i in 1:nadd) {
## newc[i, 1:(cats[(cvar[indx])[i]])] <- -as.integer(cdir[i])
## newc[i, 1:ccut[i]] <- as.integer(cdir[i])
## }
## catmat <- if (ncat == 0)
## newc
## else {
## cs <- rpfit$csplit
## ncs <- ncol(cs)
## ncc <- ncol(newc)
## if (ncs < ncc)
## cs <- cbind(cs, matrix(0, nrow(cs), ncc - ncs))
## rbind(cs, newc)
## }
## ncat <- ncat + nadd
## }
## else catmat <- rpfit$csplit
## if (nsplit == 0) {
## frame <- data.frame(row.names = 1, var = "<leaf>", n = rpfit$inode[,
## 5], wt = rpfit$dnode[, 3], dev = rpfit$dnode[, 1],
## yval = rpfit$dnode[, 4], complexity = rpfit$dnode[,
## 2], ncompete = 0, nsurrogate = 0)
## }
## else {
## temp <- ifelse(index == 0, 1, index)
## svar <- ifelse(index == 0, 0, rpfit$isplit[temp, 1])
## frame <- data.frame(row.names = rpfit$inode[, 1], var = tname[svar +
## 1], n = rpfit$inode[, 5], wt = rpfit$dnode[, 3],
## dev = rpfit$dnode[, 1], yval = rpfit$dnode[, 4],
## complexity = rpfit$dnode[, 2], ncompete = pmax(0,
## rpfit$inode[, 3] - 1), nsurrogate = rpfit$inode[,
## 4])
## }
## if (method.int == 3) {
## numclass <- init$numresp - 2
## nodeprob <- rpfit$dnode[, numclass + 5]/sum(wt)
## temp <- pmax(1, init$counts)
## temp <- rpfit$dnode[, 4 + (1:numclass)] %*% diag(init$parms$prior/temp)
## yprob <- temp/rowSums(temp)
## yval2 <- matrix(rpfit$dnode[, 4 + (0:numclass)], ncol = numclass +
## 1)
## frame$yval2 <- cbind(yval2, yprob, nodeprob)
## }
## else if (init$numresp > 1)
## frame$yval2 <- rpfit$dnode[, -(1:3), drop = FALSE]
## if (is.null(init$summary))
## stop("Initialization routine is missing the 'summary' function")
## functions <- if (is.null(init$print))
## list(summary = init$summary)
## else list(summary = init$summary, print = init$print)
## if (!is.null(init$text))
## functions <- c(functions, list(text = init$text))
## if (method == "user")
## functions <- c(functions, mlist)
## where <- rpfit$which
## names(where) <- row.names(m)
## ans <- list(frame = frame, where = where, call = Call, terms = Terms,
## cptable = t(rpfit$cptable), method = method, parms = init$parms,
## control = controls, functions = functions, numresp = init$numresp)
## if (nsplit)
## ans$splits = splits
## if (ncat > 0)
## ans$csplit <- catmat + 2
## if (nsplit)
## ans$variable.importance <- importance(ans)
## if (model) {
## ans$model <- m
## if (missing(y))
## y <- FALSE
## }
## if (y)
## ans$y <- Y
## if (x) {
## ans$x <- X
## ans$wt <- wt
## }
## ans$ordered <- isord
## if (!is.null(attr(m, "na.action")))
## ans$na.action <- attr(m, "na.action")
## if (!is.null(xlevels))
## attr(ans, "xlevels") <- xlevels
## if (method == "class")
## attr(ans, "ylevels") <- init$ylevels
## class(ans) <- "rpart"
## ans
## })(formula = .outcome ~ ., data = list(c(1, 3, 7, 8, 11, 13,
## 16, 17, 18, 20, 22, 26, 27, 34, 36, 39, 41, 42, 43, 44, 46, 50,
## 53, 55, 57, 59, 60, 61, 64, 65, 67, 69, 72, 74, 78, 79, 80, 82,
## 83, 85, 86, 88, 89, 93, 95, 96, 97, 98, 100, 103, 107, 108, 109,
## 111, 112, 113, 115, 118, 119, 120, 121, 122, 123, 124, 127, 134,
## 144, 145, 149, 150, 151, 153, 157, 160, 162, 163, 164, 166, 170,
## 171, 173, 181, 182, 183, 185, 186, 192, 193, 195, 199, 200, 201,
## 204, 208, 210, 211, 213, 214, 216, 218, 220, 224, 225, 226, 228,
## 234, 240, 243, 244, 246, 248, 250, 251, 253, 254, 257, 258, 259,
## 260, 263, 265, 267, 268, 269, 270, 271, 272, 273, 274, 277, 278,
## 279, 280, 281, 282, 283, 286, 287, 293, 295, 297, 301, 306, 310,
## 311, 314, 315, 319, 322, 328, 330, 333, 337, 338, 339, 340, 341,
## 343, 348, 350, 353, 356, 357, 358, 359, 360, 361, 362, 366, 368,
## 369, 370, 371, 374, 377, 379, 380, 381, 384, 385, 387, 392, 394,
## 396, 397, 398, 400, 401, 404, 409, 410, 411, 412, 413, 414, 416,
## 419, 420, 424, 425, 426, 428, 429, 431, 432, 433, 438, 442, 443,
## 444, 448, 453, 454, 457, 458, 459, 460, 461, 463, 465, 466, 467,
## 469, 470, 471, 473, 477, 478, 479, 480, 482, 484, 486, 488, 490,
## 493, 494, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 507,
## 511, 512, 514, 515, 520, 522, 529, 532, 533, 536, 538, 540, 543,
## 546, 547, 548, 553, 555, 557, 558, 559, 561, 562, 563, 565, 567,
## 568, 570, 573, 574, 576, 578, 581, 584, 586, 587, 588, 591, 592,
## 596, 597, 599, 600, 602, 604, 605, 606, 608, 610, 611, 615, 616,
## 617, 619, 620, 621, 622, 623, 627, 628, 629, 632, 637, 639, 640,
## 642, 644, 647, 650, 651, 656, 658, 659, 660, 661, 663, 664, 667,
## 668, 673, 674, 675, 676, 678, 679, 680, 683, 684, 687, 688, 692,
## 693, 694, 696, 701, 705, 707, 708, 712, 714, 716, 719, 720, 722,
## 724, 728, 732, 733, 734, 735, 736, 737, 738, 741, 742, 743, 747,
## 750, 751, 755, 756, 757, 758, 759, 762, 764, 765, 768, 771, 772,
## 773, 774, 775, 776, 777, 778, 779, 781, 207, 646, 148, 289, 276,
## 114, 320, 761, 422, 740, 612, 363, 485, 203, 131, 261, 749, 99,
## 130, 197, 682, 323, 290, 177, 140, 364, 455, 695, 506, 455, 189,
## 682, 643, 327, 572, 320, 709, 307, 633, 189, 66, 233, 290, 15,
## 288, 681, 142, 114, 624, 327, 58, 197, 317, 135, 388, 715, 695,
## 421, 633, 77, 66, 304, 91, 346, 364, 603, 670, 304, 31, 331,
## 66, 290, 485, 641, 90, 670, 686, 549, 203, 276, 110, 446, 643,
## 292, 383, 603, 316, 662, 110, 154, 262, 749, 209, 354, 294, 276,
## 317, 15, 572, 101, 31, 476, 521, 364, 572, 307, 582, 76, 323,
## 239, 476, 91, 485, 376, 155, 646, 58, 292, 582, 236, 451, 131,
## 292, 290, 76, 312, 405, 662, 367, 376, 76, 312, 146, 312, 256,
## 131, 154, 73, 276, 307, 191, 681, 99, 641, 506, 645, 323, 521,
## 289, 302, 513, 256, 68, 130, 135, 718, 524, 405, 116, 575, 207,
## 474, 31, 304, 239, 221, 624, 700, 316, 261, 354, 312, 583, 534,
## 449, 446, 245, 87, 66, 15, 612, 56, 364, 99, 318, 307, 455, 99,
## 304, 238, 624, 110, 91, 717, 782, 148, 221, 101, 730, 388, 191,
## 312, 236, 266, 309, 346, 238, 534, 101, 485, 196, 402, 116, 142,
## 582, 347, 130, 191, 345, 264, 276, 318, 481, 726, 73, 449, 346,
## 15, 624, 625, 524, 45, 450, 782, 749, 646, 718, 464, 245, 681,
## 152, 146, 101, 203, 68, 323, 723, 681, 682, 288, 68, 449, 135,
## 645, 700, 188, 730, 700, 101, 717, 402, 290, 513, 405, 633, 177,
## 749, 323, 367, 142, 583, 761, 191, 769, 196, 66, 721, 177, 423,
## 288, 421, 245, 239, 129, 723, 449, 717, 575, 276, 131, 66, 730,
## 582, 312, 363, 99, 686, 721, 233, 449, 154, 136, 87, 155, 761,
## 140, 196, 237, 761, 142, 730, 405, 87, 549, 45, 239, 318, 402,
## 307, 630, 760, 316, 364, 421, 207, 91, 288, 73, 363, 191, 450,
## 135, 421, 159, 641, 138, 154, 364, 317, 154, 304, 513, 152, 625,
## 206, 643, 73, 177, 485, 670, 464, 327, 383, 721, 15, 320, 143,
## 302, 545, 207, 695, 140, 290, 643, 196, 545, 715, 534, 323, 318,
## 421, 575, 726, 485, 464, 136, 155, 239, 241, 28, 76, 227, 92,
## 521, 76, 423), c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3,
## 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
## 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
## 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
## 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
## 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
## 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
## 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
## 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 4, 1, 2, 2, 1, 2,
## 4, 2, 4, 4, 2, 3, 1, 1, 1, 4, 1, 1, 1, 4, 2, 2, 1, 1, 2, 2, 4,
## 3, 2, 1, 4, 4, 2, 3, 2, 4, 2, 4, 1, 1, 1, 2, 1, 2, 4, 1, 1, 4,
## 2, 1, 1, 2, 1, 2, 4, 4, 2, 4, 1, 1, 2, 1, 2, 2, 3, 4, 2, 1, 2,
## 1, 2, 3, 4, 1, 4, 4, 3, 1, 2, 1, 2, 4, 2, 2, 3, 2, 4, 1, 1, 1,
## 4, 1, 2, 2, 2, 2, 1, 3, 1, 1, 3, 3, 2, 3, 2, 3, 1, 2, 1, 3, 1,
## 3, 2, 1, 4, 1, 2, 3, 1, 2, 1, 2, 2, 1, 2, 2, 4, 2, 2, 1, 2, 1,
## 2, 1, 1, 1, 1, 2, 2, 1, 4, 1, 4, 3, 4, 2, 3, 2, 2, 3, 1, 1, 1,
## 1, 4, 3, 2, 1, 3, 1, 3, 1, 2, 1, 1, 4, 4, 2, 1, 2, 2, 3, 3, 2,
## 2, 1, 1, 1, 1, 4, 1, 2, 1, 2, 2, 2, 1, 2, 1, 4, 1, 1, 4, 4, 1,
## 1, 1, 4, 2, 1, 2, 1, 1, 2, 2, 1, 3, 1, 3, 1, 2, 1, 1, 3, 2, 1,
## 1, 2, 1, 2, 2, 3, 4, 1, 2, 2, 1, 4, 4, 3, 1, 2, 4, 4, 4, 4, 2,
## 1, 4, 1, 1, 1, 1, 1, 2, 4, 4, 4, 2, 1, 2, 1, 4, 4, 1, 4, 4, 1,
## 4, 2, 2, 3, 2, 4, 1, 4, 2, 2, 1, 3, 4, 1, 4, 1, 1, 4, 1, 2, 2,
## 2, 1, 1, 1, 4, 2, 4, 3, 2, 1, 1, 4, 3, 2, 2, 1, 4, 4, 1, 2, 1,
## 1, 1, 1, 4, 1, 1, 1, 4, 1, 4, 2, 1, 3, 1, 1, 2, 2, 2, 4, 4, 2,
## 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 2, 2, 1, 2, 3, 1,
## 4, 1, 4, 1, 1, 3, 4, 2, 2, 2, 4, 1, 2, 1, 2, 3, 1, 4, 1, 2, 4,
## 1, 3, 4, 3, 2, 2, 2, 3, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1,
## 2), c(19, 19, 18, 19, 18, 19, 18, 18, 18, 18, 18, 18, 19, 19,
## 18, 19, 19, 18, 19, 19, 18, 18, 18, 18, 19, 19, 19, 19, 19, 18,
## 18, 24, 19, 18, 19, 20, 20, 18, 18, 20, 18, 18, 18, 19, 20, 19,
## 18, 18, 18, 18, 19, 18, 19, 18, 18, 18, 18, 18, 18, 18, 18, 18,
## 18, 18, 19, 18, 18, 18, 19, 18, 20, 19, 18, 18, 18, 18, 20, 19,
## 19, 18, 18, 20, 18, 18, 18, 19, 26, 20, 20, 19, 19, 23, 19, 19,
## 20, 19, 20, 20, 24, 20, 20, 19, 19, 18, 19, 19, 20, 19, 19, 19,
## 19, 19, 19, 20, 20, 19, 20, 19, 20, 19, 19, 20, 19, 20, 24, 22,
## 19, 20, 21, 20, 21, 19, 21, 20, 25, 19, 19, 20, 20, 20, 19, 20,
## 19, 19, 18, 19, 19, 20, 19, 19, 23, 18, 19, 19, 19, 20, 19, 20,
## 19, 22, 19, 19, 19, 21, 22, 19, 20, 18, 20, 19, 19, 21, 19, 21,
## 20, 19, 19, 20, 22, 19, 19, 19, 20, 19, 20, 19, 20, 20, 20, 19,
## 23, 19, 19, 20, 20, 19, 21, 20, 19, 21, 19, 19, 20, 20, 19, 20,
## 19, 23, 19, 19, 20, 20, 19, 19, 25, 20, 21, 19, 20, 20, 19, 20,
## 20, 21, 20, 20, 20, 20, 21, 22, 20, 20, 21, 26, 20, 20, 20, 21,
## 20, 20, 20, 20, 20, 21, 20, 21, 20, 20, 21, 20, 22, 23, 19, 21,
## 22, 21, 20, 21, 20, 20, 21, 22, 20, 22, 21, 23, 22, 21, 21, 21,
## 21, 21, 21, 22, 21, 23, 21, 22, 21, 18, 21, 25, 22, 21, 21, 21,
## 21, 21, 20, 27, 21, 22, 22, 23, 21, 23, 22, 21, 22, 21, 21, 21,
## 21, 21, 21, 21, 21, 21, 21, 22, 22, 24, 22, 22, 24, 21, 22, 21,
## 22, 25, 21, 24, 22, 21, 21, 21, 21, 22, 26, 21, 21, 21, 21, 21,
## 22, 22, 22, 22, 21, 21, 21, 20, 21, 21, 21, 21, 21, 21, 22, 22,
## 21, 21, 23, 21, 22, 22, 22, 22, 26, 22, 22, 22, 22, 30, 22, 23,
## 24, 22, 23, 22, 22, 24, 22, 23, 24, 23, 21, 22, 23, 22, 23, 22,
## 23, 22, 24, 22, 18, 21, 18, 20, 19, 18, 24, 22, 19, 21, 24, 20,
## 20, 19, 18, 19, 22, 19, 18, 20, 21, 19, 20, 18, 18, 19, 20, 21,
## 28, 20, 21, 21, 21, 22, 22, 24, 21, 19, 22, 21, 18, 19, 20, 18,
## 23, 22, 19, 18, 21, 22, 18, 20, 20, 20, 20, 21, 21, 19, 22, 19,
## 18, 20, 19, 19, 19, 22, 22, 20, 20, 19, 18, 20, 20, 21, 18, 22,
## 21, 20, 19, 19, 19, 19, 21, 19, 18, 22, 19, 22, 19, 19, 19, 22,
## 21, 22, 20, 19, 20, 18, 22, 19, 20, 20, 22, 19, 22, 19, 22, 20,
## 19, 22, 20, 19, 20, 19, 18, 21, 18, 19, 22, 19, 19, 18, 19, 20,
## 20, 19, 19, 22, 19, 19, 20, 19, 23, 19, 21, 18, 19, 20, 19, 19,
## 20, 22, 19, 21, 28, 21, 19, 22, 20, 19, 21, 21, 20, 18, 20, 21,
## 21, 19, 18, 22, 18, 20, 20, 20, 22, 21, 21, 22, 19, 19, 22, 19,
## 22, 20, 20, 19, 19, 19, 18, 18, 24, 19, 19, 19, 19, 19, 20, 19,
## 20, 21, 21, 19, 19, 21, 22, 18, 21, 19, 22, 20, 20, 19, 19, 21,
## 19, 19, 21, 20, 19, 20, 19, 19, 18, 19, 22, 19, 18, 20, 21, 19,
## 19, 19, 20, 21, 20, 20, 19, 18, 21, 21, 21, 18, 19, 22, 22, 21,
## 21, 19, 19, 22, 18, 23, 19, 19, 20, 19, 21, 22, 21, 23, 20, 20,
## 20, 21, 22, 23, 22, 22, 19, 21, 19, 20, 21, 19, 22, 18, 22, 19,
## 19, 19, 22, 22, 20, 22, 19, 18, 21, 18, 19, 23, 19, 19, 22, 19,
## 21, 20, 21, 22, 19, 18, 18, 22, 22, 19, 20, 19, 21, 21, 19, 20,
## 19, 21, 19, 18, 22, 18, 19, 23, 22, 19, 22, 19, 19, 20, 18, 22,
## 19, 19, 19, 21, 22, 19, 19, 19, 18, 19, 23, 20, 20, 20, 19, 20,
## 19, 20, 21, 19, 19, 19, 20, 19, 20, 21, 18, 21, 20, 21, 20, 18,
## 20, 22, 19, 22, 18, 21, 18, 24, 19, 19, 21, 18, 21, 18, 20, 21,
## 19, 21, 21, 20, 19, 19, 19, 22, 21, 20, 19, 21, 18, 22, 20, 18,
## 20, 24, 18, 22, 20, 19), c(1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1,
## 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1,
## 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1,
## 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0,
## 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1,
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## 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1,
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## 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0,
## 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0,
## 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1,
## 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1,
## 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0,
## 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1,
## 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1,
## 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0,
## 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1,
## 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1,
## 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1), c(1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1,
## 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1,
## 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 1), c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1,
## 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1),
## c(0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1,
## 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0,
## 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0,
## 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1,
## 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0,
## 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1,
## 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1,
## 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1,
## 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
## 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1,
## 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0,
## 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1,
## 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0,
## 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1,
## 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1,
## 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1,
## 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0,
## 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1,
## 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,
## 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
## 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1,
## 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0,
## 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1,
## 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1,
## 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1,
## 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1,
## 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0,
## 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1,
## 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1), c(1, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0,
## 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0,
## 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1,
## 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0,
## 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1,
## 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1,
## 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1,
## 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0,
## 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1,
## 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0,
## 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 0, 0, 0), c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,
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## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1,
## 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
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## 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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## 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0),
## c(1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0,
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## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
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## 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0,
## 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
## 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1,
## 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0,
## 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0,
## 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0,
## 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0,
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## 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0,
## 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0,
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## 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), c(0, 0, 1, 0, 1, 1,
## 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0,
## 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1,
## 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0,
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## 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1,
## 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1,
## 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,
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## 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0,
## 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0,
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## 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0,
## 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0,
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## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0), c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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## 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0),
## c(0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1,
## 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1,
## 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0,
## 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0,
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## 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,
## 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1,
## 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1,
## 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1,
## 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0,
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## 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1,
## 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1,
## 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1,
## 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0,
## 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0,
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## 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1), c(1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1,
## 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0,
## 1, 1, 1, 0, 1, 1), c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0,
## 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1,
## 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1,
## 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1),
## c(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
## 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0,
## 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0,
## 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1,
## 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
## 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0), c(0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0), c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
## 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
## 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0),
## c(1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1,
## 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1,
## 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1,
## 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,
## 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
## 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,
## 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1,
## 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
## 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0,
## 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1,
## 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1,
## 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0,
## 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0,
## 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0,
## 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1,
## 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0,
## 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1,
## 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1,
## 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0,
## 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1,
## 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1), c(1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
## 2, 2, 2, 2, 2, 2)), control = list(20, 7, 0, 4, 5, 2, 0,
## 30, 0))
## n= 772
##
## CP nsplit rel error
## 1 0.67357513 0 1.00000000
## 2 0.23575130 1 0.32642487
## 3 0.08290155 2 0.09067358
##
## Variable importance
## depression_severityModerate phq_score(9,14]
## 30 30
## suicidal0 anxiety_severitySevere
## 19 3
## depression_severityModerately severe gad_score(14,21]
## 3 3
## phq_score(14,19] phq_score(19,27]
## 3 3
## anxiety_severityModerate gad_score(9,14]
## 1 1
## phq_score(4,9] bmi(39.9,100]
## 1 1
##
## Node number 1: 772 observations, complexity param=0.6735751
## predicted class=0 expected loss=0.5 P(node) =1
## class counts: 386 386
## probabilities: 0.500 0.500
## left son=2 (512 obs) right son=3 (260 obs)
## Primary splits:
## phq_score(9,14] < 0.5 to the left, improve=196.01560, (0 missing)
## depression_severityModerate < 0.5 to the left, improve=196.01560, (0 missing)
## phq_score(4,9] < 0.5 to the right, improve=128.85190, (0 missing)
## depression_severityNone-minimal < 0.5 to the right, improve= 93.08682, (0 missing)
## suicidal0 < 0.5 to the right, improve= 84.76145, (0 missing)
## Surrogate splits:
## depression_severityModerate < 0.5 to the left, agree=1.000, adj=1.000, (0 split)
## phq_score(4,9] < 0.5 to the right, agree=0.675, adj=0.035, (0 split)
## gad_score(9,14] < 0.5 to the left, agree=0.675, adj=0.035, (0 split)
## anxiety_severityModerate < 0.5 to the left, agree=0.675, adj=0.035, (0 split)
## bmi(39.9,100] < 0.5 to the left, agree=0.672, adj=0.027, (0 split)
##
## Node number 2: 512 observations, complexity param=0.2357513
## predicted class=0 expected loss=0.2460938 P(node) =0.6632124
## class counts: 386 126
## probabilities: 0.754 0.246
## left son=4 (421 obs) right son=5 (91 obs)
## Primary splits:
## suicidal0 < 0.5 to the right, improve=125.80390, (0 missing)
## phq_score(14,19] < 0.5 to the left, improve=107.78070, (0 missing)
## depression_severityModerately severe < 0.5 to the left, improve=107.78070, (0 missing)
## anxiousness0 < 0.5 to the right, improve= 56.94776, (0 missing)
## gad_score(14,21] < 0.5 to the left, improve= 54.98914, (0 missing)
## Surrogate splits:
## phq_score(14,19] < 0.5 to the left, agree=0.854, adj=0.176, (0 split)
## depression_severityModerately severe < 0.5 to the left, agree=0.854, adj=0.176, (0 split)
## gad_score(14,21] < 0.5 to the left, agree=0.854, adj=0.176, (0 split)
## anxiety_severitySevere < 0.5 to the left, agree=0.854, adj=0.176, (0 split)
## phq_score(19,27] < 0.5 to the left, agree=0.852, adj=0.165, (0 split)
##
## Node number 3: 260 observations
## predicted class=1 expected loss=0 P(node) =0.3367876
## class counts: 0 260
## probabilities: 0.000 1.000
##
## Node number 4: 421 observations
## predicted class=0 expected loss=0.08313539 P(node) =0.5453368
## class counts: 386 35
## probabilities: 0.917 0.083
##
## Node number 5: 91 observations
## predicted class=1 expected loss=0 P(node) =0.1178756
## class counts: 0 91
## probabilities: 0.000 1.000#accuracy of the tree
accuracy <- tree$results$Accuracy
print(paste("Accuracy:", accuracy))## [1] "Accuracy: 0.957250082610816" "Accuracy: 0.87695289347663"
## [3] "Accuracy: 0.698166302130048"# get the average accuracy across all fold
accuracy <- mean(tree$results$Accuracy)
print(paste("Average Accuracy:", accuracy))## [1] "Average Accuracy: 0.844123092739165"predict(tree, test)## [1] 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0
## [38] 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 0
## [75] 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0
## [112] 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0
## Levels: 0 1# predict on test data
predictions <- predict(tree, test)
predictions <- factor(predictions, levels = levels(test$depressiveness))
# Proceed with creating the confusion matrix and calculating metrics
confusion <- confusionMatrix(predictions, test$depressiveness)
# Getting the accuracy from the confusion matrix
accuracy <- confusion$overall['Accuracy']
# Calculate precision
precision <- confusion$byClass["Precision"]
# Calculate recall (sensitivity)
recall <- confusion$byClass["Recall"]
# Calculate F1 score
f1_score <- confusion$byClass["F1"]
# Print the results
print(confusion)## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 0
## 1 35 0
## 0 4 97
##
## Accuracy : 0.9706
## 95% CI : (0.9264, 0.9919)
## No Information Rate : 0.7132
## P-Value [Acc > NIR] : 4.212e-15
##
## Kappa : 0.9258
##
## Mcnemar's Test P-Value : 0.1336
##
## Sensitivity : 0.8974
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9604
## Prevalence : 0.2868
## Detection Rate : 0.2574
## Detection Prevalence : 0.2574
## Balanced Accuracy : 0.9487
##
## 'Positive' Class : 1
## # add to the dataset of evalution
tree1 <- valuation_df <- data.frame(tree = "tree2", accuracy = accuracy,Precision =precision,Recall =recall ,F1=f1_score, Atrribute="Ginin index",
cv_K=5)
evaluation_df <- rbind(evaluation_df, tree1)
# visulize the tree'
fancyRpartPlot(trained_model, caption = NULL)
evaluation_df## tree accuracy Precision Recall F1 Atrribute cv_K
## Accuracy tree1 0.9705882 1 0.8974359 0.9459459 information gain 5
## Accuracy1 tree2 0.9705882 1 0.8974359 0.9459459 Ginin index 5Gain Ratio
dataset<-over
folds <- createFolds(dataset$depressiveness, k = 5) # create the folds
# control parameters
train_control <- trainControl(method = "cv", index = folds)# Compute the gain ratio of attributes for predicting the depressiveness
weights <- gain.ratio(depressiveness ~ ., data = dataset)
# Print the weights
print(weights)## attr_importance
## id 0.031906086
## school_year 0.000000000
## age 0.000000000
## gender 0.009099528
## bmi 0.013728588
## who_bmi 0.014757816
## phq_score 0.423562118
## depression_severity 0.423562118
## suicidal 0.306981398
## depression_diagnosis 0.071937073
## depression_treatment 0.046011468
## gad_score 0.107108370
## anxiety_severity 0.107108370
## anxiousness 0.156958882
## anxiety_diagnosis 0.058667581
## anxiety_treatment 0.050780281
## epworth_score 0.041232820
## sleepiness 0.028702391#build the model
tree <- train(depressiveness ~ ., data = dataset, trControl = train_control,
method = "rpart", parms = list(split = weights))trained_model <- tree$finalModel
trained_model## n= 772
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 772 386 0 (0.50000000 0.50000000)
## 2) phq_score(9,14]< 0.5 512 126 0 (0.75390625 0.24609375)
## 4) suicidal0>=0.5 421 35 0 (0.91686461 0.08313539) *
## 5) suicidal0< 0.5 91 0 1 (0.00000000 1.00000000) *
## 3) phq_score(9,14]>=0.5 260 0 1 (0.00000000 1.00000000) *trained_model$variable.importance## depression_severityModerate phq_score(9,14]
## 196.015625 196.015625
## suicidal0 anxiety_severitySevere
## 125.803852 22.119359
## depression_severityModerately severe gad_score(14,21]
## 22.119359 22.119359
## phq_score(14,19] phq_score(19,27]
## 22.119359 20.736899
## anxiety_severityModerate gad_score(9,14]
## 6.785156 6.785156
## phq_score(4,9] bmi(39.9,100]
## 6.785156 5.277344#accuracy of the tree
accuracy <- tree$results$Accuracy
print(paste("Accuracy:", accuracy))## [1] "Accuracy: 0.965678483947276" "Accuracy: 0.881846600892721"
## [3] "Accuracy: 0.699460800511925"# get the average accuracy across all fold
accuracy <- mean(tree$results$Accuracy)
print(paste("Average Accuracy:", accuracy))## [1] "Average Accuracy: 0.848995295117307"# predict on test data
predictions <- predict(tree, test)
predictions <- factor(predictions, levels = levels(test$depressiveness))
# Proceed with creating the confusion matrix and calculating metrics
confusion <- confusionMatrix(predictions, test$depressiveness)
# Getting the accuracy from the confusion matrix
accuracy <- confusion$overall['Accuracy']
# Calculate precision
precision <- confusion$byClass["Precision"]
# Calculate recall (sensitivity)
recall <- confusion$byClass["Recall"]
# Calculate F1 score
f1_score <- confusion$byClass["F1"]
# Print the results
print(confusion)## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 0
## 1 35 0
## 0 4 97
##
## Accuracy : 0.9706
## 95% CI : (0.9264, 0.9919)
## No Information Rate : 0.7132
## P-Value [Acc > NIR] : 4.212e-15
##
## Kappa : 0.9258
##
## Mcnemar's Test P-Value : 0.1336
##
## Sensitivity : 0.8974
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9604
## Prevalence : 0.2868
## Detection Rate : 0.2574
## Detection Prevalence : 0.2574
## Balanced Accuracy : 0.9487
##
## 'Positive' Class : 1
## # add to the dataset of evalution
tree1 <- valuation_df <- data.frame(tree = "tree3", accuracy = accuracy,Precision =precision,Recall =recall ,F1=f1_score, Atrribute="Gain ratio",
cv_K=5)
evaluation_df <- rbind(evaluation_df, tree1)
# visulize the tree'
fancyRpartPlot(trained_model, caption = NULL)
evaluation_df## tree accuracy Precision Recall F1 Atrribute cv_K
## Accuracy tree1 0.9705882 1 0.8974359 0.9459459 information gain 5
## Accuracy1 tree2 0.9705882 1 0.8974359 0.9459459 Ginin index 5
## Accuracy2 tree3 0.9705882 1 0.8974359 0.9459459 Gain ratio 5DT with k-validation 7 and attribute selection information gain, gain ratio , gini index
dataset<-over
folds <- createFolds(dataset$depressiveness, k = 7) # create the folds
# control parameters
train_control <- trainControl(method = "cv", index = folds)train_control## $method
## [1] "cv"
##
## $number
## [1] 10
##
## $repeats
## [1] NA
##
## $search
## [1] "grid"
##
## $p
## [1] 0.75
##
## $initialWindow
## NULL
##
## $horizon
## [1] 1
##
## $fixedWindow
## [1] TRUE
##
## $skip
## [1] 0
##
## $verboseIter
## [1] FALSE
##
## $returnData
## [1] TRUE
##
## $returnResamp
## [1] "final"
##
## $savePredictions
## [1] FALSE
##
## $classProbs
## [1] FALSE
##
## $summaryFunction
## function (data, lev = NULL, model = NULL)
## {
## if (is.character(data$obs))
## data$obs <- factor(data$obs, levels = lev)
## postResample(data[, "pred"], data[, "obs"])
## }
## <bytecode: 0x7f7aa8b0a9e8>
## <environment: namespace:caret>
##
## $selectionFunction
## [1] "best"
##
## $preProcOptions
## $preProcOptions$thresh
## [1] 0.95
##
## $preProcOptions$ICAcomp
## [1] 3
##
## $preProcOptions$k
## [1] 5
##
## $preProcOptions$freqCut
## [1] 19
##
## $preProcOptions$uniqueCut
## [1] 10
##
## $preProcOptions$cutoff
## [1] 0.9
##
##
## $sampling
## NULL
##
## $index
## $index$Fold1
## [1] 2 6 12 15 23 26 33 37 39 43 53 59 68 76 89 99 111 127
## [19] 130 132 140 160 163 167 176 180 198 203 224 225 227 237 249 261 264 267
## [37] 282 285 287 292 305 309 312 313 317 327 328 337 348 352 355 359 363 385
## [55] 386 400 405 420 422 424 439 441 477 479 482 486 487 489 492 494 499 506
## [73] 511 512 517 524 531 536 545 553 562 563 567 569 572 590 615 622 635 656
## [91] 669 672 693 696 702 709 722 730 731 737 740 744 748 752 754 758 760 763
## [109] 764 765
##
## $index$Fold2
## [1] 11 24 29 46 55 63 71 72 77 84 96 109 110 114 122 125 126 137
## [19] 139 147 152 154 159 161 183 199 201 213 221 222 228 240 248 251 253 266
## [37] 268 269 277 284 307 315 316 318 322 330 331 338 342 343 349 356 365 371
## [55] 383 392 398 406 423 427 429 446 452 456 457 459 460 462 467 483 502 503
## [73] 523 530 532 542 543 544 554 558 560 576 586 597 598 607 610 617 619 624
## [91] 636 638 644 649 650 665 674 680 682 695 697 703 705 714 724 729 736 739
## [109] 747 761 768
##
## $index$Fold3
## [1] 4 9 10 21 27 28 38 42 45 57 58 64 87 91 93 100 108 117
## [19] 120 124 172 178 179 182 190 191 200 202 212 218 220 223 229 255 265 270
## [37] 271 272 274 276 288 291 293 298 303 308 311 319 321 323 336 347 353 357
## [55] 361 390 394 404 407 426 431 434 440 458 471 472 473 478 496 498 504 513
## [73] 519 546 548 549 552 556 559 564 573 583 589 596 602 608 616 625 630 639
## [91] 640 643 651 653 662 664 666 667 671 673 678 679 683 685 688 690 715 735
## [109] 750 766
##
## $index$Fold4
## [1] 7 8 13 19 36 49 54 56 74 75 78 82 83 98 101 107 118 119
## [19] 123 131 133 134 155 157 164 168 181 193 195 196 210 216 219 235 236 244
## [37] 245 246 252 254 259 262 273 294 295 300 324 333 334 335 341 351 373 379
## [55] 381 393 408 409 410 412 414 418 419 436 450 451 454 463 465 469 480 488
## [73] 501 514 518 533 534 537 561 568 579 584 594 601 609 623 628 631 654 658
## [91] 659 660 670 676 687 689 692 698 700 721 723 734 738 741 745 746 753 756
## [109] 759 771
##
## $index$Fold5
## [1] 3 5 17 25 34 35 44 47 48 50 52 70 73 85 88 92 94 104
## [19] 105 113 121 136 144 145 146 153 158 162 165 170 175 214 226 231 233 241
## [37] 242 247 250 258 275 281 289 290 296 297 299 320 326 332 340 350 354 362
## [55] 368 370 387 388 389 399 415 432 437 444 449 466 470 474 476 484 485 495
## [73] 508 516 527 529 538 540 541 547 550 551 555 557 571 574 578 591 592 595
## [91] 603 604 606 611 613 621 626 646 647 657 668 677 694 701 707 711 718 727
## [109] 732 757 770
##
## $index$Fold6
## [1] 14 16 18 22 30 31 32 60 62 66 67 69 79 80 86 90 102 103
## [19] 115 116 128 129 135 138 141 151 173 174 177 186 189 194 197 206 208 211
## [37] 215 232 238 239 243 260 263 279 283 302 304 314 329 344 358 360 372 380
## [55] 384 391 396 397 401 403 411 425 430 435 442 443 464 475 493 515 522 525
## [73] 526 539 565 587 588 593 599 600 612 620 629 632 633 634 637 641 645 648
## [91] 652 655 661 663 675 684 704 706 708 716 717 720 725 728 733 742 743 751
## [109] 755 769
##
## $index$Fold7
## [1] 1 20 40 41 51 61 65 81 95 97 106 112 142 143 148 149 150 156
## [19] 166 169 171 184 185 187 188 192 204 205 207 209 217 230 234 256 257 278
## [37] 280 286 301 306 310 325 339 345 346 364 366 367 369 374 375 376 377 378
## [55] 382 395 402 413 416 417 421 428 433 438 445 447 448 453 455 461 468 481
## [73] 490 491 497 500 505 507 509 510 520 521 528 535 566 570 575 577 580 581
## [91] 582 585 605 614 618 627 642 681 686 691 699 710 712 713 719 726 749 762
## [109] 767 772
##
##
## $indexOut
## NULL
##
## $indexFinal
## NULL
##
## $timingSamps
## [1] 0
##
## $predictionBounds
## [1] FALSE FALSE
##
## $seeds
## [1] NA
##
## $adaptive
## $adaptive$min
## [1] 5
##
## $adaptive$alpha
## [1] 0.05
##
## $adaptive$method
## [1] "gls"
##
## $adaptive$complete
## [1] TRUE
##
##
## $trim
## [1] FALSE
##
## $allowParallel
## [1] TRUEInformation gain - k=7
#build the model
tree <- train(depressiveness ~ ., data = dataset, trControl = train_control,
method = "rpart", parms = list(split = "information"))# train result
trained_model <- tree$finalModel
trained_model## n= 772
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 772 386 0 (0.50000000 0.50000000)
## 2) phq_score(9,14]< 0.5 512 126 0 (0.75390625 0.24609375)
## 4) suicidal0>=0.5 421 35 0 (0.91686461 0.08313539) *
## 5) suicidal0< 0.5 91 0 1 (0.00000000 1.00000000) *
## 3) phq_score(9,14]>=0.5 260 0 1 (0.00000000 1.00000000) *#features importance
trained_model$variable.importance## depression_severityModerate phq_score(9,14]
## 249.412160 249.412160
## suicidal0 anxiety_severitySevere
## 165.139447 29.035507
## depression_severityModerately severe gad_score(14,21]
## 29.035507 29.035507
## phq_score(14,19] phq_score(19,27]
## 29.035507 27.220788
## anxiety_severityModerate gad_score(9,14]
## 8.633498 8.633498
## phq_score(4,9] bmi(39.9,100]
## 8.633498 6.714943#accuracy of the tree
accuracy <- tree$results$Accuracy
print(paste("Accuracy:", accuracy))## [1] "Accuracy: 0.954227028142317" "Accuracy: 0.898960651946378"
## [3] "Accuracy: 0.641849331749739"# get the average accuracy across all fold
accuracy <- mean(tree$results$Accuracy)
print(paste("Average Accuracy:", accuracy))## [1] "Average Accuracy: 0.831679003946145"# predict on test data
predictions <- predict(tree, test)
predictions <- factor(predictions, levels = levels(test$depressiveness))
# Proceed with creating the confusion matrix and calculating metrics
confusion <- confusionMatrix(predictions, test$depressiveness)
# Getting the accuracy from the confusion matrix
accuracy <- confusion$overall['Accuracy']
# Calculate precision
precision <- confusion$byClass["Precision"]
# Calculate recall (sensitivity)
recall <- confusion$byClass["Recall"]
# Calculate F1 score
f1_score <- confusion$byClass["F1"]
# Print the results
print(confusion)## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 0
## 1 35 0
## 0 4 97
##
## Accuracy : 0.9706
## 95% CI : (0.9264, 0.9919)
## No Information Rate : 0.7132
## P-Value [Acc > NIR] : 4.212e-15
##
## Kappa : 0.9258
##
## Mcnemar's Test P-Value : 0.1336
##
## Sensitivity : 0.8974
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9604
## Prevalence : 0.2868
## Detection Rate : 0.2574
## Detection Prevalence : 0.2574
## Balanced Accuracy : 0.9487
##
## 'Positive' Class : 1
## # add to the dataset of evalution
tree1 <- valuation_df <- data.frame(tree = "tree4", accuracy = accuracy,Precision =precision,Recall =recall ,F1=f1_score, Atrribute="Information Gain",
cv_K=7)
evaluation_df <- rbind(evaluation_df, tree1)
# visulize the tree'
fancyRpartPlot(trained_model, caption = NULL)
evaluation_df## tree accuracy Precision Recall F1 Atrribute cv_K
## Accuracy tree1 0.9705882 1 0.8974359 0.9459459 information gain 5
## Accuracy1 tree2 0.9705882 1 0.8974359 0.9459459 Ginin index 5
## Accuracy2 tree3 0.9705882 1 0.8974359 0.9459459 Gain ratio 5
## Accuracy3 tree4 0.9705882 1 0.8974359 0.9459459 Information Gain 7Gini index - k=7
dataset<-over
folds <- createFolds(dataset$depressiveness, k = 7) # create the folds
# control parameters
train_control <- trainControl(method = "cv", index = folds)#build the model
tree <- train(depressiveness ~ ., data = dataset, trControl = train_control,
method = "rpart", parms = list(split = "gini"))# train result
trained_model <- tree$finalModel
trained_model## n= 772
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 772 386 0 (0.50000000 0.50000000)
## 2) phq_score(9,14]< 0.5 512 126 0 (0.75390625 0.24609375)
## 4) suicidal0>=0.5 421 35 0 (0.91686461 0.08313539) *
## 5) suicidal0< 0.5 91 0 1 (0.00000000 1.00000000) *
## 3) phq_score(9,14]>=0.5 260 0 1 (0.00000000 1.00000000) *#features importance
trained_model$variable.importance## depression_severityModerate phq_score(9,14]
## 196.015625 196.015625
## suicidal0 anxiety_severitySevere
## 125.803852 22.119359
## depression_severityModerately severe gad_score(14,21]
## 22.119359 22.119359
## phq_score(14,19] phq_score(19,27]
## 22.119359 20.736899
## anxiety_severityModerate gad_score(9,14]
## 6.785156 6.785156
## phq_score(4,9] bmi(39.9,100]
## 6.785156 5.277344#accuracy of the tree
accuracy <- tree$results$Accuracy
print(paste("Accuracy:", accuracy))## [1] "Accuracy: 0.958331728192006" "Accuracy: 0.90351947096283"
## [3] "Accuracy: 0.630988020531009"# get the average accuracy across all fold
accuracy <- mean(tree$results$Accuracy)
print(paste("Average Accuracy:", accuracy))## [1] "Average Accuracy: 0.830946406561948"# predict on test data
predictions <- predict(tree, test)
predictions <- factor(predictions, levels = levels(test$depressiveness))
# Proceed with creating the confusion matrix and calculating metrics
confusion <- confusionMatrix(predictions, test$depressiveness)
# Getting the accuracy from the confusion matrix
accuracy <- confusion$overall['Accuracy']
# Calculate precision
precision <- confusion$byClass["Precision"]
# Calculate recall (sensitivity)
recall <- confusion$byClass["Recall"]
# Calculate F1 score
f1_score <- confusion$byClass["F1"]
# Print the results
print(confusion)## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 0
## 1 35 0
## 0 4 97
##
## Accuracy : 0.9706
## 95% CI : (0.9264, 0.9919)
## No Information Rate : 0.7132
## P-Value [Acc > NIR] : 4.212e-15
##
## Kappa : 0.9258
##
## Mcnemar's Test P-Value : 0.1336
##
## Sensitivity : 0.8974
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9604
## Prevalence : 0.2868
## Detection Rate : 0.2574
## Detection Prevalence : 0.2574
## Balanced Accuracy : 0.9487
##
## 'Positive' Class : 1
## # add to the dataset of evalution
tree1 <- valuation_df <- data.frame(tree = "tree5", accuracy = accuracy,Precision =precision,Recall =recall ,F1=f1_score, Atrribute="Gini index",
cv_K=7)
evaluation_df <- rbind(evaluation_df, tree1)
# visulize the tree'
fancyRpartPlot(trained_model, caption = NULL)
Gain Ratio - k=7
dataset<-under
folds <- createFolds(dataset$depressiveness, k = 7) # create the folds
# control parameters
train_control <- trainControl(method = "cv", index = folds)# Compute the gain ratio of attributes for predicting the depressiveness
weights <- gain.ratio(depressiveness ~ ., data = dataset)
# Print the weights
print(weights)## attr_importance
## id 0.00000000
## school_year 0.00000000
## age 0.00000000
## gender 0.01460764
## bmi 0.01542339
## who_bmi 0.01469843
## phq_score 0.39953942
## depression_severity 0.39953942
## suicidal 0.29789404
## depression_diagnosis 0.06653417
## depression_treatment 0.04646065
## gad_score 0.12889219
## anxiety_severity 0.12889219
## anxiousness 0.19390318
## anxiety_diagnosis 0.03413004
## anxiety_treatment 0.04157032
## epworth_score 0.04046182
## sleepiness 0.02361210#build the model
tree <- train(depressiveness ~ ., data = dataset, trControl = train_control,
method = "rpart", parms = list(split = weights))#build the model
tree <- train(depressiveness ~ ., data = dataset, trControl = train_control,
method = "rpart", parms = list(split = weights))# train result
trained_model <- tree$finalModel
trained_model## n= 310
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 310 155 0 (0.5000000 0.5000000)
## 2) phq_score(9,14]< 0.5 209 54 0 (0.7416268 0.2583732)
## 4) suicidal0>=0.5 173 18 0 (0.8959538 0.1040462) *
## 5) suicidal0< 0.5 36 0 1 (0.0000000 1.0000000) *
## 3) phq_score(9,14]>=0.5 101 0 1 (0.0000000 1.0000000) *#features importance
trained_model$variable.importance## depression_severityModerate phq_score(9,14]
## 74.9043062 74.9043062
## suicidal0 depression_severitySevere
## 47.8413585 7.9735598
## phq_score(19,27] anxiety_severitySevere
## 7.9735598 5.3157065
## epworth_score(17,24] gad_score(14,21]
## 5.3157065 5.3157065
## bmi(39.9,100] who_bmiClass III Obesity
## 1.4832536 1.4832536
## bmi(34.9,39.9] who_bmiClass II Obesity
## 0.7416268 0.7416268#accuracy of the tree
accuracy <- tree$results$Accuracy
print(paste("Accuracy:", accuracy))## [1] "Accuracy: 0.837678612114702" "Accuracy: 0.822047000618429"
## [3] "Accuracy: 0.666837548416496"# get the average accuracy across all fold
accuracy <- mean(tree$results$Accuracy)
print(paste("Average Accuracy:", accuracy))## [1] "Average Accuracy: 0.775521053716542"fancyRpartPlot(trained_model, caption = NULL)
# predict on test data
predictions <- predict(tree, test)
predictions <- factor(predictions, levels = levels(test$depressiveness))
# Proceed with creating the confusion matrix and calculating metrics
confusion <- confusionMatrix(predictions, test$depressiveness)
# Getting the accuracy from the confusion matrix
accuracy <- confusion$overall['Accuracy']
# Calculate precision
precision <- confusion$byClass["Precision"]
# Calculate recall (sensitivity)
recall <- confusion$byClass["Recall"]
# Calculate F1 score
f1_score <- confusion$byClass["F1"]
# Print the results
print(confusion)## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 0
## 1 35 0
## 0 4 97
##
## Accuracy : 0.9706
## 95% CI : (0.9264, 0.9919)
## No Information Rate : 0.7132
## P-Value [Acc > NIR] : 4.212e-15
##
## Kappa : 0.9258
##
## Mcnemar's Test P-Value : 0.1336
##
## Sensitivity : 0.8974
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9604
## Prevalence : 0.2868
## Detection Rate : 0.2574
## Detection Prevalence : 0.2574
## Balanced Accuracy : 0.9487
##
## 'Positive' Class : 1
## # add to the dataset of evalution
tree1 <- valuation_df <- data.frame(tree = "tree6", accuracy = accuracy,Precision =precision,Recall =recall ,F1=f1_score, Atrribute="Gain ratio",
cv_K=7)
evaluation_df <- rbind(evaluation_df, tree1)
# visulize the tree'
fancyRpartPlot(trained_model, caption = NULL)
DT with k-validation 10 and attribute selection information gain, gain ratio , gini index
information gain - k=10
dataset<-under
folds <- createFolds(dataset$depressiveness, k = 10) # create the folds
# control parameters
train_control <- trainControl(method = "cv", index = folds)
#build the model
tree <- train(depressiveness ~ ., data = dataset, trControl = train_control,
method = "rpart", parms = list(split = "information"))
# train result
trained_model <- tree$finalModel
trained_model## n= 310
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 310 155 0 (0.5000000 0.5000000)
## 2) phq_score(9,14]< 0.5 209 54 0 (0.7416268 0.2583732)
## 4) suicidal0>=0.5 173 18 0 (0.8959538 0.1040462) *
## 5) suicidal0< 0.5 36 0 1 (0.0000000 1.0000000) *
## 3) phq_score(9,14]>=0.5 101 0 1 (0.0000000 1.0000000) *#features importance
trained_model$variable.importance## depression_severityModerate phq_score(9,14]
## 95.4637989 95.4637989
## suicidal0 depression_severitySevere
## 61.6499659 10.2749943
## phq_score(19,27] anxiety_severitySevere
## 10.2749943 6.8499962
## epworth_score(17,24] gad_score(14,21]
## 6.8499962 6.8499962
## bmi(39.9,100] who_bmiClass III Obesity
## 1.8903723 1.8903723
## bmi(34.9,39.9] who_bmiClass II Obesity
## 0.9451861 0.9451861#accuracy of the tree
accuracy <- tree$results$Accuracy
print(paste("Accuracy:", accuracy))## [1] "Accuracy: 0.795326080149705" "Accuracy: 0.791754651578277"
## [3] "Accuracy: 0.736235638217537"# get the average accuracy across all fold
accuracy <- mean(tree$results$Accuracy)
print(paste("Average Accuracy:", accuracy))## [1] "Average Accuracy: 0.774438789981839"# predict on test data
predictions <- predict(tree, test)
predictions <- factor(predictions, levels = levels(test$depressiveness))
# Proceed with creating the confusion matrix and calculating metrics
confusion <- confusionMatrix(predictions, test$depressiveness)
# Getting the accuracy from the confusion matrix
accuracy <- confusion$overall['Accuracy']
# Calculate precision
precision <- confusion$byClass["Precision"]
# Calculate recall (sensitivity)
recall <- confusion$byClass["Recall"]
# Calculate F1 score
f1_score <- confusion$byClass["F1"]
# Print the results
print(confusion)## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 0
## 1 35 0
## 0 4 97
##
## Accuracy : 0.9706
## 95% CI : (0.9264, 0.9919)
## No Information Rate : 0.7132
## P-Value [Acc > NIR] : 4.212e-15
##
## Kappa : 0.9258
##
## Mcnemar's Test P-Value : 0.1336
##
## Sensitivity : 0.8974
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9604
## Prevalence : 0.2868
## Detection Rate : 0.2574
## Detection Prevalence : 0.2574
## Balanced Accuracy : 0.9487
##
## 'Positive' Class : 1
## # add to the dataset of evalution
tree1 <- valuation_df <- data.frame(tree = "tree7", accuracy = accuracy,Precision =precision,Recall =recall ,F1=f1_score, Atrribute=" information Gain ",
cv_K=10)
evaluation_df <- rbind(evaluation_df, tree1)
# visulize the tree'
fancyRpartPlot(trained_model, caption = NULL)
Gini index - k=10
dataset<-under
folds <- createFolds(dataset$depressiveness, k = 10) # create the folds
# control parameters
train_control <- trainControl(method = "cv", index = folds)
#build the model
tree <- train(depressiveness ~ ., data = dataset, trControl = train_control,
method = "rpart", parms = list(split = "gini"))
# train result
trained_model <- tree$finalModel
trained_model## n= 310
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 310 155 0 (0.5000000 0.5000000)
## 2) phq_score(9,14]< 0.5 209 54 0 (0.7416268 0.2583732) *
## 3) phq_score(9,14]>=0.5 101 0 1 (0.0000000 1.0000000) *#features importance
trained_model$variable.importance## depression_severityModerate phq_score(9,14]
## 74.9043062 74.9043062
## bmi(39.9,100] who_bmiClass III Obesity
## 1.4832536 1.4832536
## bmi(34.9,39.9] who_bmiClass II Obesity
## 0.7416268 0.7416268#accuracy of the tree
accuracy <- tree$results$Accuracy
print(paste("Accuracy:", accuracy))## [1] "Accuracy: 0.783517784850461" "Accuracy: 0.798571548291321"
## [3] "Accuracy: 0.693912050083436"# get the average accuracy across all fold
accuracy <- mean(tree$results$Accuracy)
print(paste("Average Accuracy:", accuracy))## [1] "Average Accuracy: 0.758667127741739"# predict on test data
predictions <- predict(tree, test)
predictions <- factor(predictions, levels = levels(test$depressiveness))
# Proceed with creating the confusion matrix and calculating metrics
confusion <- confusionMatrix(predictions, test$depressiveness)
# Getting the accuracy from the confusion matrix
accuracy <- confusion$overall['Accuracy']
# Calculate precision
precision <- confusion$byClass["Precision"]
# Calculate recall (sensitivity)
recall <- confusion$byClass["Recall"]
# Calculate F1 score
f1_score <- confusion$byClass["F1"]
# Print the results
print(confusion)## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 0
## 1 29 0
## 0 10 97
##
## Accuracy : 0.9265
## 95% CI : (0.8689, 0.9642)
## No Information Rate : 0.7132
## P-Value [Acc > NIR] : 6.355e-10
##
## Kappa : 0.8053
##
## Mcnemar's Test P-Value : 0.004427
##
## Sensitivity : 0.7436
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9065
## Prevalence : 0.2868
## Detection Rate : 0.2132
## Detection Prevalence : 0.2132
## Balanced Accuracy : 0.8718
##
## 'Positive' Class : 1
## # add to the dataset of evalution
tree1 <- valuation_df <- data.frame(tree = "tree8", accuracy = accuracy,Precision =precision,Recall =recall ,F1=f1_score, Atrribute="Gini index",
cv_K=10)
evaluation_df <- rbind(evaluation_df, tree1)
# visulize the tree'
fancyRpartPlot(trained_model, caption = NULL)
Gain ratio - k=10
dataset<-under
folds <- createFolds(dataset$depressiveness, k = 10) # create the folds
# control parameters
train_control <- trainControl(method = "cv", index = folds)
# Compute the gain ratio of attributes for predicting the depressiveness
weights <- gain.ratio(depressiveness ~ ., data = dataset)
# Print the weights
print(weights)## attr_importance
## id 0.00000000
## school_year 0.00000000
## age 0.00000000
## gender 0.01460764
## bmi 0.01542339
## who_bmi 0.01469843
## phq_score 0.39953942
## depression_severity 0.39953942
## suicidal 0.29789404
## depression_diagnosis 0.06653417
## depression_treatment 0.04646065
## gad_score 0.12889219
## anxiety_severity 0.12889219
## anxiousness 0.19390318
## anxiety_diagnosis 0.03413004
## anxiety_treatment 0.04157032
## epworth_score 0.04046182
## sleepiness 0.02361210#build the model
tree <- train(depressiveness ~ ., data = dataset, trControl = train_control,
method = "rpart", parms = list(split = weights))# train result
trained_model <- tree$finalModel
trained_model## n= 310
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 310 155 0 (0.5000000 0.5000000)
## 2) phq_score(9,14]< 0.5 209 54 0 (0.7416268 0.2583732)
## 4) suicidal0>=0.5 173 18 0 (0.8959538 0.1040462) *
## 5) suicidal0< 0.5 36 0 1 (0.0000000 1.0000000) *
## 3) phq_score(9,14]>=0.5 101 0 1 (0.0000000 1.0000000) *#features importance
trained_model$variable.importance## depression_severityModerate phq_score(9,14]
## 74.9043062 74.9043062
## suicidal0 depression_severitySevere
## 47.8413585 7.9735598
## phq_score(19,27] anxiety_severitySevere
## 7.9735598 5.3157065
## epworth_score(17,24] gad_score(14,21]
## 5.3157065 5.3157065
## bmi(39.9,100] who_bmiClass III Obesity
## 1.4832536 1.4832536
## bmi(34.9,39.9] who_bmiClass II Obesity
## 0.7416268 0.7416268#accuracy of the tree
accuracy <- tree$results$Accuracy
print(paste("Accuracy:", accuracy))## [1] "Accuracy: 0.831188312023193" "Accuracy: 0.793553903421042"
## [3] "Accuracy: 0.627127044907853"# get the average accuracy across all fold
accuracy <- mean(tree$results$Accuracy)
print(paste("Average Accuracy:", accuracy))## [1] "Average Accuracy: 0.750623086784029"# predict on test data
predictions <- predict(tree, test)
predictions <- factor(predictions, levels = levels(test$depressiveness))
# Proceed with creating the confusion matrix and calculating metrics
confusion <- confusionMatrix(predictions, test$depressiveness)
# Calculate precision
precision <- confusion$byClass["Precision"]
# Getting the accuracy from the confusion matrix
accuracy <- confusion$overall['Accuracy']
# Calculate recall (sensitivity)
recall <- confusion$byClass["Recall"]
# Calculate F1 score
f1_score <- confusion$byClass["F1"]
# Print the results
print(confusion)## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 0
## 1 35 0
## 0 4 97
##
## Accuracy : 0.9706
## 95% CI : (0.9264, 0.9919)
## No Information Rate : 0.7132
## P-Value [Acc > NIR] : 4.212e-15
##
## Kappa : 0.9258
##
## Mcnemar's Test P-Value : 0.1336
##
## Sensitivity : 0.8974
## Specificity : 1.0000
## Pos Pred Value : 1.0000
## Neg Pred Value : 0.9604
## Prevalence : 0.2868
## Detection Rate : 0.2574
## Detection Prevalence : 0.2574
## Balanced Accuracy : 0.9487
##
## 'Positive' Class : 1
## # add to the dataset of evalution
tree1 <- valuation_df <- data.frame(tree = "tree9", accuracy = accuracy,Precision =precision,Recall =recall ,F1=f1_score, Atrribute="Gain ratio",
cv_K=10)
evaluation_df <- rbind(evaluation_df, tree1)
# visulize the tree'
fancyRpartPlot(trained_model, caption = NULL)
evaluation_df## tree accuracy Precision Recall F1 Atrribute cv_K
## Accuracy tree1 0.9705882 1 0.8974359 0.9459459 information gain 5
## Accuracy1 tree2 0.9705882 1 0.8974359 0.9459459 Ginin index 5
## Accuracy2 tree3 0.9705882 1 0.8974359 0.9459459 Gain ratio 5
## Accuracy3 tree4 0.9705882 1 0.8974359 0.9459459 Information Gain 7
## Accuracy4 tree5 0.9705882 1 0.8974359 0.9459459 Gini index 7
## Accuracy5 tree6 0.9705882 1 0.8974359 0.9459459 Gain ratio 7
## Accuracy6 tree7 0.9705882 1 0.8974359 0.9459459 information Gain 10
## Accuracy7 tree8 0.9264706 1 0.7435897 0.8529412 Gini index 10
## Accuracy8 tree9 0.9705882 1 0.8974359 0.9459459 Gain ratio 10This table displays the results of classification using various methods for each K.
information gain : +—————————————-+——————-+—————-+—————————–+ | | K=5 | K=7 | K=10 | +:======================================:+:=================:+:==============:+:===========================:+ | precision | 0.95 | 0.95 | 0.95 | +—————————————-+——————-+—————-+—————————–+ | sensitivity | 1 | 1 | 1 | +—————————————-+——————-+—————-+—————————–+ | specificity | 1 | 0.948 | 0.9487 | +—————————————-+——————-+—————-+—————————–+ | Accuracy | 89.42% |88.91% | 88.59% | +—————————————-+——————-+—————-+—————————–+
Gain ratio: +—————————————-+——————-+—————-+—————————–+ | | K=5 | K=7 | K=10 | +:======================================:+:=================:+:==============:+:===========================:+ | precision | 0.95 | 0.95 | 0.95 | +—————————————-+——————-+—————-+—————————–+ | sensitivity | 1 | 1 | 1 | +—————————————-+——————-+—————-+—————————–+ | specificity | 1 | 0.948 | 0.9487 | +—————————————-+——————-+—————-+—————————–+ | Accuracy |90.85% |88.11% | 86.04% | +—————————————-+——————-+—————-+—————————–+
Gini index: +—————————————-+——————-+—————-+—————————–+ | | K=5 | K=7 | K=10 | +:======================================:+:=================:+:==============:+:===========================:+ | precision | 0.95 | 0.95 | 0.95 | +—————————————-+——————-+—————-+—————————–+ | sensitivity | 1 | 1 | 1 | +—————————————-+——————-+—————-+—————————–+ | specificity | 1 | 0.948 | 0.9487 | +—————————————-+——————-+—————-+—————————–+ | Accuracy |90.95% | 89.47% | 87.37% | +—————————————-+——————-+—————-+—————————–+
Clustering
# include the libraries and import the dataset
library('superml')## Loading required package: R6library(cluster)
library(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa# import the dataset
df<-datasethead(df,10)## id school_year age gender bmi who_bmi phq_score
## 1 469 3 20 male (18.4,24.9] Normal (4,9]
## 2 220 1 20 male (18.4,24.9] Normal (0,4]
## 3 311 2 18 male (24.9,29.9] Overweight (0,4]
## 4 280 2 21 male (18.4,24.9] Normal (4,9]
## 5 254 1 20 female (18.4,24.9] Normal (0,4]
## 6 683 4 22 male (24.9,29.9] Overweight (0,4]
## 7 501 3 20 female (18.4,24.9] Normal (4,9]
## 8 211 1 19 male (18.4,24.9] Normal (0,4]
## 9 651 4 21 female (18,18.4] Underweight (4,9]
## 10 200 1 19 female (18.4,24.9] Normal (0,4]
## depression_severity depressiveness suicidal depression_diagnosis
## 1 Mild 0 0 0
## 2 None-minimal 0 0 0
## 3 None-minimal 0 0 0
## 4 Mild 0 0 0
## 5 None-minimal 0 0 1
## 6 None-minimal 0 0 0
## 7 Mild 0 0 0
## 8 None-minimal 0 0 0
## 9 Mild 0 0 0
## 10 None-minimal 0 0 0
## depression_treatment gad_score anxiety_severity anxiousness
## 1 0 (0,4] None-minimal 0
## 2 0 (0,4] None-minimal 0
## 3 0 (4,9] Mild 0
## 4 0 (4,9] Mild 0
## 5 1 (4,9] Mild 0
## 6 0 (0,4] None-minimal 0
## 7 0 (0,4] None-minimal 0
## 8 0 (0,4] None-minimal 0
## 9 0 (4,9] Mild 0
## 10 0 (0,4] None-minimal 0
## anxiety_diagnosis anxiety_treatment epworth_score sleepiness
## 1 0 0 (0,10] 0
## 2 0 0 (0,10] 0
## 3 0 0 (0,10] 0
## 4 0 0 (0,10] 0
## 5 0 0 (10,14] 1
## 6 0 0 (0,10] 0
## 7 0 0 (0,10] 0
## 8 0 0 (0,10] 0
## 9 0 0 (0,10] 0
## 10 0 0 (0,10] 0str(df)## 'data.frame': 310 obs. of 19 variables:
## $ id : num 469 220 311 280 254 683 501 211 651 200 ...
## $ school_year : num 3 1 2 2 1 4 3 1 4 1 ...
## $ age : num 20 20 18 21 20 22 20 19 21 19 ...
## $ gender : chr "male" "male" "male" "male" ...
## $ bmi : Factor w/ 6 levels "(18,18.4]","(18.4,24.9]",..: 2 2 3 2 2 3 2 2 1 2 ...
## $ who_bmi : chr "Normal" "Normal" "Overweight" "Normal" ...
## $ phq_score : Factor w/ 5 levels "(0,4]","(4,9]",..: 2 1 1 2 1 1 2 1 2 1 ...
## $ depression_severity : chr "Mild" "None-minimal" "None-minimal" "Mild" ...
## $ depressiveness : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ suicidal : Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ depression_diagnosis: Factor w/ 2 levels "1","0": 2 2 2 2 1 2 2 2 2 2 ...
## $ depression_treatment: Factor w/ 2 levels "1","0": 2 2 2 2 1 2 2 2 2 2 ...
## $ gad_score : Factor w/ 4 levels "(0,4]","(4,9]",..: 1 1 2 2 2 1 1 1 2 1 ...
## $ anxiety_severity : chr "None-minimal" "None-minimal" "Mild" "Mild" ...
## $ anxiousness : Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ anxiety_diagnosis : Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ anxiety_treatment : Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ epworth_score : Factor w/ 4 levels "(0,10]","(10,14]",..: 1 1 1 1 2 1 1 1 1 1 ...
## $ sleepiness : Factor w/ 2 levels "1","0": 2 2 2 2 1 2 2 2 2 2 ...let’s prepocess the data before applay clustering as well as kmeans deal only with numeric we need to convert factor and chr to numeric value, like labels encoding
# using label encoder
encoding <- LabelEncoder$new()# Identify categorical columns
categorical_cols <- dataset %>%
select_if(is.character) %>%
names()categorical_cols## [1] "gender" "who_bmi" "depression_severity"
## [4] "anxiety_severity"# Convert categorical columns to factors
df[categorical_cols] <- lapply(df[categorical_cols], as.factor)str(df)## 'data.frame': 310 obs. of 19 variables:
## $ id : num 469 220 311 280 254 683 501 211 651 200 ...
## $ school_year : num 3 1 2 2 1 4 3 1 4 1 ...
## $ age : num 20 20 18 21 20 22 20 19 21 19 ...
## $ gender : Factor w/ 2 levels "female","male": 2 2 2 2 1 2 1 2 1 1 ...
## $ bmi : Factor w/ 6 levels "(18,18.4]","(18.4,24.9]",..: 2 2 3 2 2 3 2 2 1 2 ...
## $ who_bmi : Factor w/ 6 levels "Class I Obesity",..: 4 4 5 4 4 5 4 4 6 4 ...
## $ phq_score : Factor w/ 5 levels "(0,4]","(4,9]",..: 2 1 1 2 1 1 2 1 2 1 ...
## $ depression_severity : Factor w/ 5 levels "Mild","Moderate",..: 1 4 4 1 4 4 1 4 1 4 ...
## $ depressiveness : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ suicidal : Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ depression_diagnosis: Factor w/ 2 levels "1","0": 2 2 2 2 1 2 2 2 2 2 ...
## $ depression_treatment: Factor w/ 2 levels "1","0": 2 2 2 2 1 2 2 2 2 2 ...
## $ gad_score : Factor w/ 4 levels "(0,4]","(4,9]",..: 1 1 2 2 2 1 1 1 2 1 ...
## $ anxiety_severity : Factor w/ 4 levels "Mild","Moderate",..: 3 3 1 1 1 3 3 3 1 3 ...
## $ anxiousness : Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ anxiety_diagnosis : Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ anxiety_treatment : Factor w/ 2 levels "1","0": 2 2 2 2 2 2 2 2 2 2 ...
## $ epworth_score : Factor w/ 4 levels "(0,10]","(10,14]",..: 1 1 1 1 2 1 1 1 1 1 ...
## $ sleepiness : Factor w/ 2 levels "1","0": 2 2 2 2 1 2 2 2 2 2 ...categorical_cols <- dataset %>%
select_if(is.factor) %>%
names()
categorical_cols## [1] "bmi" "phq_score" "depressiveness"
## [4] "suicidal" "depression_diagnosis" "depression_treatment"
## [7] "gad_score" "anxiousness" "anxiety_diagnosis"
## [10] "anxiety_treatment" "epworth_score" "sleepiness"for (col in categorical_cols)
{
# Fit the LabelEncoder object to the data frame column
encoding$fit(df[[col]])
# Transform the data frame column using the LabelEncoder object
encoded_col <- encoding$fit_transform(df[[col]])
# Assign the encoded column to the data frame
df[[col]] <- encoded_col
}head(df,10)## id school_year age gender bmi who_bmi phq_score depression_severity
## 1 469 3 20 male 1 Normal 1 Mild
## 2 220 1 20 male 1 Normal 0 None-minimal
## 3 311 2 18 male 2 Overweight 0 None-minimal
## 4 280 2 21 male 1 Normal 1 Mild
## 5 254 1 20 female 1 Normal 0 None-minimal
## 6 683 4 22 male 2 Overweight 0 None-minimal
## 7 501 3 20 female 1 Normal 1 Mild
## 8 211 1 19 male 1 Normal 0 None-minimal
## 9 651 4 21 female 0 Underweight 1 Mild
## 10 200 1 19 female 1 Normal 0 None-minimal
## depressiveness suicidal depression_diagnosis depression_treatment gad_score
## 1 0 1 1 1 0
## 2 0 1 1 1 0
## 3 0 1 1 1 1
## 4 0 1 1 1 1
## 5 0 1 0 0 1
## 6 0 1 1 1 0
## 7 0 1 1 1 0
## 8 0 1 1 1 0
## 9 0 1 1 1 1
## 10 0 1 1 1 0
## anxiety_severity anxiousness anxiety_diagnosis anxiety_treatment
## 1 None-minimal 1 1 1
## 2 None-minimal 1 1 1
## 3 Mild 1 1 1
## 4 Mild 1 1 1
## 5 Mild 1 1 1
## 6 None-minimal 1 1 1
## 7 None-minimal 1 1 1
## 8 None-minimal 1 1 1
## 9 Mild 1 1 1
## 10 None-minimal 1 1 1
## epworth_score sleepiness
## 1 0 1
## 2 0 1
## 3 0 1
## 4 0 1
## 5 1 0
## 6 0 1
## 7 0 1
## 8 0 1
## 9 0 1
## 10 0 1# still some data has not changed lets convert them manually
encoding$fit(df$gender)
# Transform the data frame column using the LabelEncoder object
encoded_col <- encoding$fit_transform(df$gender)
# Assign the encoded column to the data frame
df$gender <- encoded_col# still some data has not changed lets convert them manually
encoding$fit(df$depression_severity)
# Transform the data frame column using the LabelEncoder object
encoded_col <- encoding$fit_transform(df$depression_severity)
# Assign the encoded column to the data frame
df$depression_severity <- encoded_col
# still some data has not changed lets convert them manually
encoding$fit(df$who_bmi)
# Transform the data frame column using the LabelEncoder object
encoded_col <- encoding$fit_transform(df$who_bmi)
# Assign the encoded column to the data frame
df$who_bmi <- encoded_col
# still some data has not changed lets convert them manually
encoding$fit(df$anxiety_severity)
# Transform the data frame column using the LabelEncoder object
encoded_col <- encoding$fit_transform(df$anxiety_severity)
# Assign the encoded column to the data frame
df$anxiety_severity <- encoded_colhead(df)## id school_year age gender bmi who_bmi phq_score depression_severity
## 1 469 3 20 1 1 3 1 0
## 2 220 1 20 1 1 3 0 3
## 3 311 2 18 1 2 4 0 3
## 4 280 2 21 1 1 3 1 0
## 5 254 1 20 0 1 3 0 3
## 6 683 4 22 1 2 4 0 3
## depressiveness suicidal depression_diagnosis depression_treatment gad_score
## 1 0 1 1 1 0
## 2 0 1 1 1 0
## 3 0 1 1 1 1
## 4 0 1 1 1 1
## 5 0 1 0 0 1
## 6 0 1 1 1 0
## anxiety_severity anxiousness anxiety_diagnosis anxiety_treatment
## 1 2 1 1 1
## 2 2 1 1 1
## 3 0 1 1 1
## 4 0 1 1 1
## 5 0 1 1 1
## 6 2 1 1 1
## epworth_score sleepiness
## 1 0 1
## 2 0 1
## 3 0 1
## 4 0 1
## 5 1 0
## 6 0 1# lets spilt the data to target will not be used for clustering , also id not relvant to the case
target <- data.frame(depressiveness = df$depressiveness)
predictors <- df[, -c(1,9)]
head(predictors)## school_year age gender bmi who_bmi phq_score depression_severity suicidal
## 1 3 20 1 1 3 1 0 1
## 2 1 20 1 1 3 0 3 1
## 3 2 18 1 2 4 0 3 1
## 4 2 21 1 1 3 1 0 1
## 5 1 20 0 1 3 0 3 1
## 6 4 22 1 2 4 0 3 1
## depression_diagnosis depression_treatment gad_score anxiety_severity
## 1 1 1 0 2
## 2 1 1 0 2
## 3 1 1 1 0
## 4 1 1 1 0
## 5 0 0 1 0
## 6 1 1 0 2
## anxiousness anxiety_diagnosis anxiety_treatment epworth_score sleepiness
## 1 1 1 1 0 1
## 2 1 1 1 0 1
## 3 1 1 1 0 1
## 4 1 1 1 0 1
## 5 1 1 1 1 0
## 6 1 1 1 0 1Define a function to compute BCubed precision and recall
bcubed <- function(cluster, category) {
# Check the input arguments
if (length(cluster) != length(category)) {
stop("cluster and category must have the same length")
}
if (any(is.na(cluster)) || any(is.na(category))) {
stop("cluster and category must not contain NA values")
}
# Convert cluster and category to factors
cluster <- factor(cluster)
category <- factor(category)
# Initialize the precision and recall vectors
precision <- numeric(length(cluster))
recall <- numeric(length(cluster))
# Loop over each item
for (i in 1:length(cluster)) {
# Find the items in the same cluster as the current item
same_cluster <- which(cluster == cluster[i])
# Find the items in the same category as the current item
same_category <- which(category == category[i])
# Compute the precision and recall for the current item
precision[i] <- length(intersect(same_cluster, same_category)) / length(same_cluster)
recall[i] <- length(intersect(same_cluster, same_category)) / length(same_category)
}
# Return the average precision and recall
return(c(precision = mean(precision), recall = mean(recall)))
}determining k
Elbow method
This method determines the number of clusters according to the turning point in a curve, the curve is plotted using the total within-cluster sum of square (WSS) as in y-axis , and No. clusters in x-axis
fviz_nbclust(df, kmeans, method = "wss") +
geom_vline(xintercept = 4, linetype = 2)+
labs(subtitle = "Elbow method")
k=4 ##### Silhouette method
Now we will apply Silhouette method to find the optimal number of clusters k, we will also plot a graph where x-axis represent the number of clusters and y-axis represent the average Silhouette coefficient
fviz_nbclust(df, kmeans, method = "silhouette")+
labs(subtitle = "Silhouette method")
k=2
As shown, the number of clusters k that represents the turning point in the curve is 4, so we will use it for clustering.
Lastly, we will use k=3 since it acheives the second highest average Silhouette coefficient, and since it’s in the middle between 2 and 4 it will strike a balance between having too few clusters (k=2), and having several clusters (k=4), Thus, this choice will have an acceptable acuuracy.
Cluster with k=4
#perform k-means clustering with k = 4 clusters
km <- kmeans(predictors, centers = 4, nstart = 25)
#view results
km## K-means clustering with 4 clusters of sizes 60, 110, 53, 87
##
## Cluster means:
## school_year age gender bmi who_bmi phq_score
## 1 2.166667 19.95000 0.7166667 1.366667 3.083333 0.000000
## 2 1.618182 19.23636 0.4636364 1.427273 3.018182 1.572727
## 3 1.754717 19.77358 0.2641509 1.415094 3.320755 2.622642
## 4 3.471264 21.98851 0.4827586 1.402299 3.298851 1.356322
## depression_severity suicidal depression_diagnosis depression_treatment
## 1 3.0000000 0.9833333 0.9500000 0.9500000
## 2 0.5818182 0.8181818 0.9181818 0.9090909
## 3 1.7547170 0.6415094 0.8301887 0.8679245
## 4 0.8620690 0.8505747 0.8045977 0.8965517
## gad_score anxiety_severity anxiousness anxiety_diagnosis anxiety_treatment
## 1 0.2333333 1.5833333 0.9833333 0.9000000 0.9166667
## 2 1.1545455 0.7818182 0.6363636 0.9181818 0.9090909
## 3 2.8679245 2.7358491 0.0000000 0.8679245 0.8490566
## 4 1.0919540 0.5172414 0.7816092 0.8505747 0.9080460
## epworth_score sleepiness
## 1 0.0500000 0.9333333
## 2 0.2454545 0.7454545
## 3 0.6981132 0.5471698
## 4 0.1379310 0.8045977
##
## Clustering vector:
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
## 2 1 1 4 1 1 2 1 4 1 2 2 1 1 1 3 1 2 4 2
## 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
## 2 1 1 2 1 1 1 4 4 2 4 2 2 1 2 1 4 4 2 1
## 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
## 1 2 1 2 2 1 1 1 2 1 4 2 4 1 2 1 2 1 2 1
## 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
## 4 4 2 4 2 2 4 1 2 1 4 4 4 4 1 2 4 4 4 1
## 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
## 2 4 2 2 1 4 4 2 2 1 3 2 4 1 2 4 1 4 2 1
## 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
## 1 1 2 1 4 4 1 4 1 2 2 2 4 4 1 4 1 4 1 1
## 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
## 1 4 1 2 4 1 2 4 4 1 2 4 1 4 2 2 1 2 4 1
## 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160
## 2 2 2 1 4 1 4 4 1 1 1 3 4 1 4 3 2 3 3 2
## 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
## 2 2 2 2 3 2 2 2 2 2 3 2 3 2 2 3 3 3 2 2
## 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
## 2 3 3 2 3 3 2 2 3 2 2 3 2 3 3 3 2 3 2 3
## 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220
## 2 3 2 2 2 3 3 3 4 2 4 3 3 3 2 2 2 3 3 4
## 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240
## 3 2 3 3 2 2 3 2 2 3 3 2 4 2 4 2 2 2 2 4
## 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260
## 2 3 2 2 3 3 2 2 2 3 2 2 2 2 2 2 2 3 2 2
## 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280
## 2 2 2 4 3 3 4 3 3 4 2 3 4 4 4 4 4 4 4 3
## 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300
## 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4
## 301 302 303 304 305 306 307 308 309 310
## 4 4 4 1 4 3 4 3 4 3
##
## Within cluster sum of squares by cluster:
## [1] 359.4333 660.6455 449.3585 600.8276
## (between_SS / total_SS = 42.0 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"#plot results of k-means
fviz_cluster(km, data =predictors )
#decrase the cluster by 1 cause on label encoding we start with 0
nc<-km$cluster-1# bcubed precision and recall
bcubed(nc, df$depressiveness)## precision recall
## 0.6618718 0.3322789#Within-cluster sum of squares wss
wss <- km$tot.withinss
print(wss)## [1] 2070.265#average silhouette for each clusters
avg_sil <- silhouette(km$cluster,dist(df))
fviz_silhouette(avg_sil)## cluster size ave.sil.width
## 1 1 60 -0.40
## 2 2 110 0.06
## 3 3 53 -0.20
## 4 4 87 0.42
we can conclude from the graph and the results where k=4 is that the performance is worse than k=2 and k=3, because there is a noticeable overlapping between clusters. Also, the clusers’ space is pretty wide which results in a large distance between objects in the same cluster. In addition, the recall is relatively low which might be a result of the overlapping and large distances between data objects. Furthermore, the Precision is high . We can also note that the WSS is the lowest indicating a lower compactness of clusters. Lastly, the average silhouette width is 0.03which is low reflecting high inter-cluster similarity.
Cluster with k=3
#perform k-means clustering with k = 3 clusters
km <- kmeans(predictors, centers = 3, nstart = 25)
#view results
km## K-means clustering with 3 clusters of sizes 54, 147, 109
##
## Cluster means:
## school_year age gender bmi who_bmi phq_score
## 1 1.777778 19.79630 0.2777778 1.407407 3.314815 2.629630
## 2 1.571429 19.18367 0.5102041 1.394558 2.972789 1.176871
## 3 3.449541 21.88073 0.5504587 1.422018 3.339450 1.055046
## depression_severity suicidal depression_diagnosis depression_treatment
## 1 1.759259 0.6481481 0.8148148 0.8518519
## 2 1.190476 0.8639456 0.9183673 0.9115646
## 3 1.302752 0.8715596 0.8532110 0.9266055
## gad_score anxiety_severity anxiousness anxiety_diagnosis anxiety_treatment
## 1 2.8518519 2.7037037 0.0000000 0.8703704 0.8333333
## 2 0.9387755 0.9387755 0.7278912 0.9183673 0.9115646
## 3 0.8807339 0.7981651 0.8256881 0.8532110 0.9174312
## epworth_score sleepiness
## 1 0.6851852 0.5370370
## 2 0.2040816 0.7959184
## 3 0.1100917 0.8348624
##
## Clustering vector:
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
## 2 2 2 3 2 3 2 2 3 2 2 2 2 3 2 1 2 2 3 2
## 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
## 2 3 3 2 3 2 2 3 3 2 3 2 2 2 2 2 3 3 2 3
## 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
## 3 2 2 2 2 2 2 2 2 3 3 2 3 2 2 3 2 2 2 2
## 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
## 3 3 2 3 2 2 3 3 2 2 3 3 3 3 2 2 3 3 3 2
## 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
## 2 3 2 2 3 3 3 2 2 3 1 2 3 2 2 3 2 3 2 3
## 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
## 2 2 2 2 3 3 2 3 2 2 2 2 3 3 3 3 3 3 3 3
## 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
## 3 3 3 2 3 2 2 3 3 3 2 3 3 3 2 2 2 2 3 2
## 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160
## 2 2 2 2 3 2 3 3 3 2 2 1 3 2 3 1 2 1 1 2
## 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
## 2 2 2 2 1 2 2 2 2 2 1 2 1 2 2 1 1 1 2 2
## 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
## 2 1 1 2 1 1 2 2 1 2 2 1 2 1 1 1 2 1 2 1
## 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220
## 2 1 2 2 2 1 1 1 3 2 3 1 1 1 2 2 2 1 1 3
## 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240
## 1 2 1 1 2 2 1 2 2 1 1 2 3 2 3 2 2 2 2 3
## 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260
## 2 1 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2 1 2 2
## 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280
## 2 2 2 3 1 1 3 1 1 1 2 1 3 3 3 3 3 3 3 1
## 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300
## 3 3 3 3 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3
## 301 302 303 304 305 306 307 308 309 310
## 3 3 3 3 3 1 3 1 3 1
##
## Within cluster sum of squares by cluster:
## [1] 460.0926 1098.6395 816.6789
## (between_SS / total_SS = 33.5 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"#plot results of k-means
fviz_cluster(km, data = predictors)
#decrase the cluster by 1 cause on label encoding we start with 0
nc<-km$cluster-1# bcubed precision and recall
bcubed(nc, df$depressiveness)## precision recall
## 0.5844431 0.4149844#Within-cluster sum of squares wss
wss <- km$tot.withinss
print(wss)## [1] 2375.411#average silhouette for each clusters
avg_sil <- silhouette(km$cluster,dist(df))
fviz_silhouette(avg_sil)## cluster size ave.sil.width
## 1 1 54 -0.22
## 2 2 147 0.06
## 3 3 109 0.52
we can conclude from the graph and the results where k=3 is that the performance worse than k=2, because there is overlapping between clusters. In addition, the recall is relatively low , However, the Precision is lower thn k=4 . We can also note that the WSS indicates an intermidiate compactness of clusters, and that objects in a cluster are to some extent similar to one another. Lastly, the average silhouette width is 0.13 which reflects high inter-cluster similarity.
Cluster with k=2
#perform k-means clustering with k = 2 clusters
km <- kmeans(predictors, centers = 2, nstart = 25)
#view results
km## K-means clustering with 2 clusters of sizes 132, 178
##
## Cluster means:
## school_year age gender bmi who_bmi phq_score
## 1 3.340909 21.74242 0.5303030 1.424242 3.250000 1.204545
## 2 1.471910 19.12360 0.4494382 1.393258 3.095506 1.522472
## depression_severity suicidal depression_diagnosis depression_treatment
## 1 1.378788 0.8712121 0.8560606 0.9242424
## 2 1.292135 0.7977528 0.8932584 0.8932584
## gad_score anxiety_severity anxiousness anxiety_diagnosis anxiety_treatment
## 1 1.022727 0.9924242 0.7651515 0.8560606 0.8939394
## 2 1.421348 1.3483146 0.5393258 0.9101124 0.9044944
## epworth_score sleepiness
## 1 0.2121212 0.8030303
## 2 0.2865169 0.7359551
##
## Clustering vector:
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
## 1 2 2 1 2 1 1 2 1 2 2 2 2 1 2 2 2 2 1 2
## 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
## 2 1 1 2 1 1 2 1 1 2 1 2 2 2 2 2 1 1 2 1
## 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
## 1 2 2 2 2 2 2 1 2 1 1 2 1 1 2 1 2 2 2 2
## 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
## 1 1 2 1 2 2 1 1 2 2 1 1 1 1 2 2 1 1 1 2
## 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
## 2 1 2 2 1 1 1 2 2 1 2 2 1 2 1 1 2 1 2 1
## 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
## 2 2 2 2 1 1 2 1 2 2 1 2 1 1 1 1 1 1 1 1
## 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
## 1 1 1 2 1 2 2 1 1 1 2 1 1 1 2 2 1 2 1 2
## 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160
## 2 2 2 2 1 2 1 1 1 2 2 2 1 2 1 2 2 2 2 2
## 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
## 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2
## 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220
## 2 2 2 2 2 1 2 2 1 2 1 2 2 2 2 2 2 2 2 1
## 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240
## 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 2 2 1
## 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260
## 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
## 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280
## 1 2 1 1 1 1 1 2 2 1 2 2 1 1 1 1 1 1 1 1
## 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 301 302 303 304 305 306 307 308 309 310
## 1 1 1 1 1 1 1 1 1 1
##
## Within cluster sum of squares by cluster:
## [1] 1198.992 1550.360
## (between_SS / total_SS = 23.0 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"#plot results of k-means
fviz_cluster(km, data = predictors)
#decrase the cluster by 1 cause on label encoding we start with 0
nc<-km$cluster-1# bcubed precision and recall
bcubed(nc, df$depressiveness)## precision recall
## 0.5085121 0.5193340#Within-cluster sum of squares wss
wss <- km$tot.withinss
print(wss)## [1] 2749.352#average silhouette for each clusters
avg_sil <- silhouette(km$cluster,dist(df))
fviz_silhouette(avg_sil)## cluster size ave.sil.width
## 1 1 132 0.48
## 2 2 178 0.46
we can conclude from the graph and the results that the k=2 is the optimal k, since there is less overlapping between the two clusters. Also, the recall is relatively high and is the highest among the k’s chosen, the Precision is low (0.28) which could be duo to presence of outliers or sensitivity to Initial Centroid. We can also note that the WSS is 5680, indicating a good compactness of clusters, and that objects in a cluster are similar to one another noting that the higher the k, the lower the WSS. Lastly, the average silhouette width is 0.46 which is considered high reflecting high intra-cluster similarity.
Clustering results
This table displays the results of clustering using various methods for each K.
| K=2 | K=3 | K=4 | ||
|---|---|---|---|---|
| Average Silhouette width | 0.46 | 0.13 | 0.03 | |
| total within-cluster sum of square | 5680.407 | 4825.322 | 4247.212 | |
| BCubed precision | 0.5940060 | 0.6421454 | 0.7039766 | |
| BCubed recall | 0.5193949 | 0.3959195 | 0.3276772 | |
| visual |  |
 |
 |
Based on these metrics, we can assess the performance of each K value:
Average Silhouette Width: The highest value is achieved at K = 2 (0.46), indicating that the clusters are relatively well-separated (not sparse) compared to the other K values.
Total Within-Cluster Sum of Squares: The lowest value is observed at K = 4 (4247.212), indicating better cluster compactness compared to K= 2 and K = 3.
BCubed Precision and Recall: precision highest at K = 4, recall highest at k=2 suggesting a better match between the clustering assignments and the ground truth or desired clustering structure.
Comparison and Conclusion:
Clustering:
Clustering with K=2 has the highest silhouette width, indicating well-separated clusters. As K increases, the silhouette width decreases, and the within-cluster sum of square decreases, suggesting more compact clusters. BCubed precision and recall show varying trends with K, indicating trade-offs between precision and recall.
Classification: The classification model shows consistent precision, sensitivity, and specificity across different values of K. Accuracy decreases as K increases, indicating better performance with fewer clusters.
In this study, the classification algorithms consistently exhibit superior performance in accurately predicting outcomes based on the provided features. While clustering techniques may uncover inherent patterns and groupings within the data, their effectiveness in predicting specific classes is not as pronounced as observed in the classification results. Therefore, considering the metrics such as information gain, which include precision, sensitivity, specificity, and accuracy, it becomes evident that classification is the more suitable approach for this dataset and problem. The classification algorithms consistently achieve high precision, sensitivity, specificity, and accuracy across different values of K, outperforming the clustering algorithms evaluated with metrics such as silhouette width, within-cluster sum of squares, BCubed precision, and BCubed recall.
Findings
Discussing our results and findings: We employed both supervised and unsupervised learning techniques for our data analysis, specifically focusing on classification and clustering. as we mentioned before, our dataset represents the collage students’ data to predict the probability of a university student to develop depressiveness in order to make people have the proper preventive measures that help them to make their lives better.
Therefore, we applied the data mining tasks which are classification and clustering. In the realm of classification, we utilized a decision tree algorithm, which is a recursive method that generates a tree structure with leaf nodes representing final decisions.
Our model’s primary task was to predict the class label for (depressiveness), with two possible categories: TRUE and FALSE. This prediction is made on the rest attributes , including age, gender, BMI, WHO BMI, PHQ score, depression severity, suicidal, depression diagnosis, depression treatment, GAD score, anxiety severity, anxiousness, anxiety diagnosis, anxiety treatment, Empworth score, and sleepiness. In order to split our dataset into two distinct sets: the Training set and the Testing set. we used the Cross validation method and tried 3 different sizes (10,7,5) and applied 3 attribute selection method for each size (gain ratio, gini index, information gain) which results in 9 trees. First tree, resulting from k=5 and information gain, accuracy=89.42% Second tree, resulting from k=5 and gini index, accuracy=90.85% Third tree, resulting from k=5 and Gain ratio, accuracy=90.95% Fourth tree, resulting from k=7 and information gain, accuracy=88.91% Fifth tree, resulting from k=7 and gini index, accuracy=88.11% Sixth tree, resulting from k=7 and gain ratio, accuracy=89.47% Seventh tree, resulting from k=10 and information gain, accuracy=88.59% eighth tree, resulting from k=10 and gini index, accuracy=86.04% Ninth tree, resulting from k=10 and gain ratio, accuracy=87.37%
After calculating the average accuracy for each tree, we found that the third model has the best accuracy which means that most tuples were correctly classified. In the case of clustering, as it is unsupervised learning, we did not use a class label for implementing the cluster. We removed the class label attribute “depressiveness” and used all other attributes in clustering (age, gender, BMI, who_bmo, PHQ score, depression_severity, suicidal, depression_diagnosis, depression_treatment, GAD Score, anxiety_severity, anxiousness, anxiety_diagnosis, anxiety_treatment, EPWORTH Score, and sleepiness), all of which are different data types. We implemented the K-mean algorithm for clustering, which produces K clusters, with each cluster represented by the center point and each object assigned to the nearest cluster.
We iteratively recalculated the center and reassigned objects until the center point of each cluster did not change. To implement the clustering technique, We encoded the categorical values we want to use in clustering into numerical values, and removed the attributes that are irrelevant like student id. then we defined functions to calculate the average BCubed precision and recall. we used the elbow method to determine the optimal number of clusters, which gave us a result of k=5. we will experiment clustering with k=5, k=4 ,k=3. From the cluster plot we see that in k=5,4,3 clusters are close and overlapping (there are a lot of similarities between the data objects) The silhouette coefficient measured between all data are very small and some are even negative in all k=5,4,3. The average precision and recall found show that As the number of clusters decrease the precision decreases and recall increases.
We also calculated the difference between the actual results and our clustering results ,k=3 had a higher difference than k=4. And k=5 had a higher difference than k=3 . k=4 had the lowest difference thus is a better option than the other models. At the end, we evaluated our models by measuring the average accuracy to choose the most effective model.
Refrences
[1]K. Mazidi, “RPubs - Data Mining: Classification with Decision Trees,” RPubs, 2016. [Online]. Available: https://rpubs.com/kjmazidi/195428. [Accessed: Dec. 02, 2023] [2]C. Guild, “RPubs - Classification and Regression Trees (CART) in R,” RPubs, 2021. [Online]. Available: https://rpubs.com/camguild/803096. [Accessed: Dec. 02, 2023] [3]S. BJUT, “Depression and anxiety data,” Kaggle, Jul. 29, 2022. [Online]. Available: https://www.kaggle.com/datasets/shahzadahmad0402/depression-and-anxiety-data. [Accessed: Dec. 02, 2023]